- Tytuł:
- Semi-Heyting Algebras and Identities of Associative Type
- Autorzy:
-
Cornejo, Juan M.
Sankappanavar, Hanamantagouda P. - Powiązania:
- https://bibliotekanauki.pl/articles/749914.pdf
- Data publikacji:
- 2019
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
semi-Heyting algebra
Heyting algebra
identity of associative type
subvariety of associative type - Opis:
- An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties with Heyting algebras. An identity of associative type of length 3 is a groupoid identity, both sides of which contain the same three (distinct) variables that occur in any order and that are grouped in one of the two (obvious) ways. A subvariety of ℋ is of associative type of length 3 if it is defined by a single identity of associative type of length 3. In this paper we describe all the distinct subvarieties of the variety ℋ of asociative type of length 3. Our main result shows that there are 3 such subvarities of ℋ.
- Źródło:
-
Bulletin of the Section of Logic; 2019, 48, 2
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł