A note on regular De Morgan semi-Heyting algebras

• Autorzy: Sankappanavar H. P.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this note is two-fold. Firstly, we prove that the variety RDMSH1 of regular De Morgan semi-Heyting algebras of level 1 satisfies Stone identity and present (equational) axiomatizations for several subvarieties of RDMSH1. Secondly, using our earlier results published in 2014, we give a concrete description of the lattice of subvarieties of the variety RDQDStSH1 of regular dually quasi-De Morgan Stone semi-Heyting algebras that contains RDMSH1. Furthermore, we prove that every subvariety of RDQDStSH1, and hence of RDMSH1, has Amalgamation Property. The note concludes with some open problems for further investigation.

Słowa kluczowe

EN

regular De Morgan semi-Heyting algebra of level 1; lattice of subvarieties; amalgamation property; discriminator variety; simple; subdirectly irreducible; equational bases

PL

algebra De Morgana; równanie bazowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 3
• Strony: 252--256
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Sankappanavar H. P.

Bibliografia

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• [10] H. P. Sankappanavar, Heyting algebras with a dual lattice endomorphism, Z. Math. Logik Grundlag. Math. 33 (1987), 565–573.
• [11] H. P. Sankappanavar, Semi-De Morgan algebras, J. Symbolic Logic 52 (1987), 712–724.
• [12] H. P. Sankappanavar, Semi-Heyting algebras: An abstraction from Heyting algebras, Actas del IX Congreso Dr. A. Monteiro (2007), 33–66.
• [13] H. P. Sankappanavar, Semi-Heyting algebras II, in preparation.
• [14] H. P. Sankappanavar, Expansions of Semi-Heyting algebras. I: Discriminator varieties, Studia Logica 98(1–2) (2011), 27–81.
• [15] H. P. Sankappanavar, Dually quasi-De Morgan Stone semi-Heyting algebras I, Regularity, Categories and General Algebraic Structures with Applications 2 (2014), 47–64.
• [16] H. P. Sankappanavar, Dually quasi-De Morgan Stone semi-Heyting algebras II, Regularity, Categories and General Algebraic Structures with Applications 2 (2014), 65–82.
• [17] H. P. Sankappanavar, Expansions of Semi-Heyting algebras, II, in preparation.
• [18] J, Varlet, A regular variety of type <2,2,1,1,0,0>, Algebra Universalis 2 (1972), 218–223.
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.