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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.

Subdirectly irreducible fibered automata, Part 2

Mućka A.

Demonstratio Mathematica

2011

Vol. 44, nr 1

1-15

An earlier paper characterized all subdirectly irreducible permutational fibered automata. This paper characterizes all subdirectly irreducible fibered automata which are not permutational. The characterization is both graphtheoretical and algebraic.

Subdirectly irreducible fibered automata

Mućka A.

Demonstratio Mathematica

2010

Vol. 43, nr 4

739-753

A permutational automaton is a fibered automaton with one-element event set or an empty state space. This paper characterizes all subdirectly irreducible permutational automata.

A note on configurence uniformity for single algebras

Chajda I., Länger H.

Demonstratio Mathematica

2004

Vol. 37, nr 1

9--11

It is proved that though for varieties congruence uniformity implies congruence regularity this is not the case with infinite algebras.