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Equational bases for p-compatible identities

100%

Penner P. , Wismath S. L.

2010

tom 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).

A note on regular De Morgan semi-Heyting algebras

51%

Sankappanavar H. P.

2016

tom 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.