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Wyświetlanie 1-15 z 22
Tytuł:
A scheme for congruence semidistributivity
Autorzy:
Chajda, Ivan
Horváth, Eszter
Powiązania:
https://bibliotekanauki.pl/articles/728970.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
∧ -semidistributivity
generalized semidistribitive law
triangular scheme
Opis:
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 1; 13-18
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
All maximal completely regular submonoids of $Hyp_G(2)$
Autorzy:
Kunama, Pornpimol
Leeratanavalee, Sorasak
Powiązania:
https://bibliotekanauki.pl/articles/38119704.pdf
Data publikacji:
2017-06-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized hypersubstitution
regular element
completely regular
Opis:
In this paper we consider mappings σ which map the binary operation symbol f to the term σ (f) which do not necessarily preserve the arity. These mapping are called generalized hypersubstitutions of type τ = (2) and we denote the set of all these generalized hypersubstitutions of type τ = (2) by HypG(2). The set HypG(2) together with a binary operation defined on this set and the identity generalized hypersubstitution which maps f to the term f(x1, x2) forms a monoid. In this paper, we determine all maximal completely regular submonoids of this monoid.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2017, 37, 1; 105-114
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
M-solid generalized non-deterministic varieties
Autorzy:
Lekkoksung, Somsak
Powiązania:
https://bibliotekanauki.pl/articles/728876.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized non-deterministic hypersubstitution
conjugate pair of additive closure operators
M-solid generalized non-deterministic variety
Opis:
A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2016, 36, 1; 25-43
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ring-like structures with unique symmetric difference related to quantum logic
Autorzy:
Dorninger, Dietmar
Länger, Helmut
Maczyński, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/729037.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized Boolean quasiring
symmetric difference
quantum logic
Opis:
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 2; 239-253
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Holomorph of generalized Bol loops II
Autorzy:
Jaíyéiọlá, Tèmítọ́pẹ́
Popoola, Bolaji
Powiązania:
https://bibliotekanauki.pl/articles/729179.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized Bol loop
holomorph of a loop
Opis:
The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some algebraic properties and commutative diagrams are established for a RIPL whose holomorph is a GBL.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2015, 35, 1; 59-78
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
All completely regular elements in $Hyp_{G}(n)$
Autorzy:
Boonmee, Ampika
Leeratanavalee, Sorasak
Powiązania:
https://bibliotekanauki.pl/articles/729081.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized hypersubstitution
regular element
completely regular element
Opis:
In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties.
Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In this paper, we determine the set of all completely regular elements of this monoid of type τ=(n).
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 2; 211-219
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some distributivities in GBbi-QRs characterizing Boolean rings
Autorzy:
Kaleta, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/728918.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
quasigroup
generalized Boolean bi-quasiring
generalized Boolean quasiring
Boolean ring
ring-like structure
axiomatic quantum mechanics
quantum logic
Opis:
This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 115-124
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boolean matrices ... neither Boolean nor matrices
Autorzy:
Ricci, Gabriele
Powiązania:
https://bibliotekanauki.pl/articles/728832.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
universal matrix
functional application
generalized matrix
analytic monoid
Opis:
Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 141-151
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pre-strongly solid varieties of commutative semigroups
Autorzy:
Phuapong, Sarawut
Leeratanavalee, Sorasak
Powiązania:
https://bibliotekanauki.pl/articles/728995.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
generalized hypersubstitution
pre-strongly solid variety
commutative semigroup
Opis:
Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the greatest pre-strongly solid variety of commutative semigroups.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2011, 31, 1; 27-45
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The positive and generalized discriminators dont exist
Autorzy:
Pinus, A.
Powiązania:
https://bibliotekanauki.pl/articles/728842.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
discriminator function
positive conditional term
generalized conditional term
Opis:
In this paper it is proved that there does not exist a function for the language of positive and generalized conditional terms that behaves the same as the discriminator for the language of conditional terms.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 1; 121-128
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Clifford congruences on generalized quasi-orthodox GV-semigroups
Autorzy:
Maity, Sunil
Powiązania:
https://bibliotekanauki.pl/articles/729073.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Clifford semigroup
Clifford congruence
generalized quasi-orthodox semigroup
Opis:
A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. A completely π-regular semigroup S is said to be a GV-semigroup if all the regular elements of S are completely regular. The present paper is devoted to the study of generalized quasi-orthodox GV-semigroups and least Clifford congruences on them.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2013, 33, 2; 137-145
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The monoid of generalized hypersubstitutions of type τ = (n)
Autorzy:
Puninagool, Wattapong
Leeratanavalee, Sorasak
Powiązania:
https://bibliotekanauki.pl/articles/729031.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
monoid
regular elements
idempotent elements
Green's relations
generalized hypersubstitution
Opis:
A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green's relations, have been studied for type (n) by S.L. Wismath.
A generalized hypersubstitution of type τ=(n) is a mapping σ which takes the n-ary operation symbol f to a term σ(f) which does not necessarily preserve the arity. Any such σ can be inductively extended to a map σ̂ on the set of all terms of type τ=(n), and any two such extensions can be composed in a natural way. Thus, the set $Hyp_{G}(n)$ of all generalized hypersubstitutions of type τ=(n) forms a monoid. In this paper we study the semigroup properties of $Hyp_{G}(n)$. In particular, we characterize the idempotent and regular generalized hypersubstitutions, and describe some classes under Green's relations of this monoid.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 2; 173-191
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized derivations in prime rings and Banach algebras
Autorzy:
Ali, Asma
Dhara, Basudeb
Khan, Shahoor
Powiązania:
https://bibliotekanauki.pl/articles/729205.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
prime ring
generalized derivation
extended centroid
Utumi quotient ring
Opis:
Let R be a prime ring with extended centroid C, F a generalized derivation of R and n ≥ 1, m≥ 1 fixed integers. In this paper we study the situations:
1. $(F(x∘y))^m = (x∘y)ⁿ$ for all x,y ∈ I, where I is a nonzero ideal of R;
2. (F(x∘y))ⁿ=(x∘y)ⁿ for all x,y ∈ I, where I is a nonzero right ideal of R.
Moreover, we also investigate the situation in semiprime rings and Banach algebras.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2014, 34, 1; 125-138
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized inflations and null extensions
Autorzy:
Wang, Qiang
Wismath, Shelly
Powiązania:
https://bibliotekanauki.pl/articles/729115.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
inflation
generalized inflation
null extension
variety of semigroups
bands
Opis:
An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element, but where the new elements are allowed to act like different elements of the base, depending on the context in which they are used. Such generalized inflations of semigroups are closely related to both inflations and null extensions. Clarke and Monzo proved that for a semigroup base algebra which is a union of groups, any semigroup null extension must be a generalized inflation, so that the concepts of null extension and generalized inflation coincide in the case of unions of groups. As a consequence, the collection of all associative generalized inflations formed from algebras in a variety of unions of groups also forms a variety.
In this paper we define the concept of a generalized inflation for any type of algebra. In particular, we allow for generalized inflations of semigroups which are no longer semigroups themselves. After some general results about such generalized inflations, we characterize for several varieties of bands which null extensions of algebras in the variety are generalized inflations, and which of these are associative. These characterizations are used to produce examples which answer, in our more general setting, several of the open questions posed by Clarke and Monzo.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 2; 225-249
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The vector cross product from an algebraic point of view
Autorzy:
Trenkler, Götz
Powiązania:
https://bibliotekanauki.pl/articles/728770.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vector cross product
generalized inverse
Moore-Penrose inverse
linear equations
Opis:
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 67-82
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 22

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