Opis

• Tytuł:
  Semi-Heyting Algebras and Identities of Associative Type
• Twórca:
  Cornejo, Juan M.;
  Sankappanavar, Hanamantagouda P.
• Współtwórca:
  Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, Argentina;
  Department of Mathematics, State University of New York, New Paltz, U.S.A.;
  jmcornejo@uns.edu.ar;
  sankapph@newpaltz.edu
• 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. SH 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 SH 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 SH of asociative type of length 3. Our main result shows that there are 3 such subvarities of SH.;
  Consejo Nacional de Investigaciones Cientificas y Tecnicas;
  Universidad Nacional del Sur
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.;
  http://creativecommons.org/licenses/by-nc-nd/4.0
• Data:
  2019.10.13;
  2019
• Typ:
  Article
• Język:
  angielski
• Format:
  application/pdf
• Wydawca:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relacja:
  Bulletin of the Section of Logic; 2;
  48
• Temat i słowa kluczowe:
  semi-Heyting algebra;
  Heyting algebra;
  identity of associative type;
  subvariety of associative type;
  03G25;
  06D20;
  06D15;
  08B26;
  08B15
• Identyfikator:
  0138-0680;
  http://hdl.handle.net/11089/30601 ;
  2449-836X;
  10.18778/0138-0680.48.2.03
• Dostawca danych:
  Repozytorium Uniwersytetu Łódzkiego
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