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A note on regular De Morgan semi-Heyting algebras

Sankappanavar H. P.

Demonstratio Mathematica

2016

Vol. 49, nr 3

252--256

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.

Equational bases for p-compatible identities

Penner P., Wismath S. L.

Demonstratio Mathematica

2010

Vol. 43, nr 3

511-518

A number of syntactical properties of identities, such as regularity, nor- mality, k-normality, externality and P-compatibility of identities have been extensively studied. We develop here a technique for producing from a basis for a variety V with certain idempotent terms a basis for the variety P(V), the smallest P-compatible variety to contain V. When V is finitely based, so is P(V).