Pseudo Basic Algebras
Ivan Chajda, Miroslav Kolarik and Jan Krnavek
Since basic algebras are equivalent to bounded lattices with sectional antitone involutions, it motivated us to study an algebraic counterpart of semilattices with sectional switching involutions. These algebras are called pseudo basic algebras. They are determined by four independent identities and hence the class of these algebras forms a variety. Several basic properties of these algebras are presented and a particular interest is devoted to pseudo basic algebras whose main involution is even antitone (so-called strict pseudo basic algebras) and to those whose binary operation is commutative. Congruence properties of the varieties of these algebras are investigated.
Keywords: Sectional switching involution, join-semilattice, basic algebra, pseudo basic algebra, congruence regularity, arithmeticity.
MS Classification: 06A12, 06D35, 03G25, 08B05, 08B10