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    Wyświetlanie 1-6 z 6
    Tytuł:
    Hyperidentities in associative graph algebras
    Autorzy:
    Poomsa-ard, Tiang
    Powiązania:
    https://bibliotekanauki.pl/articles/728812.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    identities
    hyperidentities
    associative graph algebras
    terms
    Opis:
    Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity s ≈ t if the correspondinggraph algebra A(G) satisfies s ≈ t. A graph G is called associative if the corresponding graph algebra A(G) satisfies the equation (xy)z ≈ x(yz). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A̲ if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A.
    In this paper we characterize associative graph algebras, identities in associative graph algebras and hyperidentities in associative graph algebras.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 169-182
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Lattices of relative colour-families and antivarieties
    Autorzy:
    Kravchenko, Aleksandr
    Powiązania:
    https://bibliotekanauki.pl/articles/728898.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    colour-family
    antivariety
    lattice of antivarieties
    meet decomposition
    basis for anti-identities
    Opis:
    We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices of colour-families are considered. A criterion is found for existence of irredundant meet decompositions. A connection is found between meet decompositions and bases for anti-identities.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2007, 27, 1; 123-139
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three
    Autorzy:
    Sandu, Nicolae
    Powiązania:
    https://bibliotekanauki.pl/articles/728912.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    nfinite independent system of identities
    alternative commutative algebra
    solvable algebra
    commutative Moufang loop
    Opis:
    Let ₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let ₂ be the subvariety of the variety ₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety ₃ ∩ ₂₂. Therefore we infer that ₃ ∩ ₂₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in ₃ ∩ ₂₂.
    It is worth mentioning that these results were announced in 1999 in works of the international conference "Loops’99" (Prague).
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 5-30
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)
    Autorzy:
    Anantpinitwatna, Apinant
    Poomsa-ard, Tiang
    Powiązania:
    https://bibliotekanauki.pl/articles/728744.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    varieties
    biregular leftmost graph varieties
    identities
    term
    hyperidentity
    M-hyperidentity
    binary algebra
    graph algebra
    Opis:
    Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra $\underline{A(G)}$ satisfies s ≈ t. A class of graph algebras V is called a graph variety if $V = Mod_g Σ$ where Σ is a subset of T(X) × T(X). A graph variety $V' = Mod_gΣ'$ is called a biregular leftmost graph variety if Σ' is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety V if $\underline{A(G)}$ satisfies s ≈ t for all G ∈ V. An identity s ≈ t of a variety V is called a hyperidentity of a graph algebra $\underline{A(G)}$, G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations of $\underline{A(G)}$ of the appropriate arity, the resulting identities hold in $\underline{A(G)}$. An identity s ≈ t of a variety V is called an M-hyperidentity of a graph algebra $\underline{A(G)}$, G ∈ V whenever the operation symbols occuring in s and t are replaced by any term operations in a subgroupoid M of term operations of $\underline{A(G)}$ of the appropriate arity, the resulting identities hold in $\underline{A(G)}$.
    In this paper we characterize special M-hyperidentities in each biregular leftmost graph variety. For identities, varieties and other basic concepts of universal algebra see e.g. [3].
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2009, 29, 2; 81-107
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    k-Normalization and (k+1)-level inflation of varieties
    Autorzy:
    Cheng, Valerie
    Wismath, Shelly
    Powiązania:
    https://bibliotekanauki.pl/articles/728838.pdf
    Data publikacji:
    2008
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    k-normal identities
    k-normalization of a variety
    (k+1)-level inflation of algebras
    Opis:
    Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety V, there is a least k-normal variety $N_k(V)$ containing V, the variety determined by the set of all k-normal identities of V. The concept of k-normalization was introduced by K. Denecke and S.L. Wismath in [5], and an algebraic characterization of the elements of $N_k(V)$ in terms of the algebras in V was given in [4]. In [1] a simplified version of this characterization of $N_k(V)$ was given, in the special case of the 2-normalization of the variety V of all lattices, using a construction called the 3-level inflation of a lattice. In this paper we show that the analogous (k+1)-level inflation can be used to characterize the algebras of $N_k(V)$ for any variety V having a unary term which satisfies two technical conditions. This includes any variety V which satisfies x ≈ t(x) for some unary term t of depth at least k, and in particular any variety, such as the variety of lattices, which satisfies an idempotent identity.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 1; 49-62
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the structure and zero divisors of the Cayley-Dickson sedenion algebra
    Autorzy:
    Cawagas, Raoul
    Powiązania:
    https://bibliotekanauki.pl/articles/729117.pdf
    Data publikacji:
    2004
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    sedenions
    subalgebras
    zero divisors
    octonions
    quasi-octonions
    quaternions
    Cayley-Dickson process
    Fenyves identities
    Opis:
    The algebras ℂ (complex numbers), ℍ (quaternions), and (octonions) are real division algebras obtained from the real numbers ℝ by a doubling procedure called the Cayley-Dickson Process. By doubling ℝ (dim 1), we obtain ℂ (dim 2), then ℂ produces ℍ (dim 4), and ℍ yields (dim 8). The next doubling process applied to then yields an algebra (dim 16) called the sedenions. This study deals with the subalgebra structure of the sedenion algebra and its zero divisors. In particular, it shows that has subalgebras isomorphic to ℝ, ℂ, ℍ, , and a newly identified algebra ̃ called the quasi-octonions that contains the zero-divisors of .
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 2; 251-265
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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