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- Title
Commutative Deductive Systems of Pseudo-M Algebras.
- Authors
WALENDZIAK, ANDRZEJ
- Abstract
We investigate the property of commutativity for various generalizations of pseudo-BCK algebras (pseudo-M, pseudo-RM, pseudo-RML, pseudo-aRML** algebras and many others). We give an axiom system for commutative pseudo-aRML** algebras and show that every such algebra (A,→,⤳, 1) is a join-semilattice with respect to the associated join operation V given by x V y = (x → y) ⤳ y. We define the commutative deductive systems of pseudo-M algebras and prove that a pseudo-aRML** algebra with the additional condition (pD) is commutative if and only if each of its deductive systems is commutative. We introduce the notion of BB-deductive system and then we construct the quotient algebra A/D of a pseudo-RM algebra A via a closed BBdeductive system D of A. Finally, we show that a BB-deductive system D of a pseudo-RML algebra A with (pD) is commutative if and only if A/D is a commutative pseudo-aRML** algebra.
- Subjects
ALGEBRA
- Publication
Journal of Multiple-Valued Logic & Soft Computing, 2022, Vol 39, Issue 2-4, p159
- ISSN
1542-3980
- Publication type
Article