Order varieties generated by ∨-semilattices of finite width

Varieties of Implicative Semilattices

Varieties Generated by Certain Models of Reversible Finite Automata

Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata. In this paper we consider some of the algebraic properties of RFA, namely the varieties these automata generate. Consequently, we obtain a characterization of the boolean closure of the classes of languages recognized by thes...

Varieties generated by T-norms

We are concerned with the variety T of algebras of type (2,2,2,0,0) generated by the algebra (I,◦), where I = ([0,1],∧,∨,0,1) is the unit interval with minimum and maximum determined by the usual order and.◦ 6 = ∧ is a continuous t-norm. We have shown that a strict t-norm and a nilpotent t-norm, and in fact any continuous t-norm except minimum, generate the same variety. Moreover, this variety ...

Levi-Properties Generated by Varieties

Levi-properties were first introduced by L. C. Kappe and are modeled after groups investigated by F. W. Levi where conjugates commute. Let X be a group theoretic class. A group is in the derived class L(X) if the normal closure of each element in the group is an X -group. The property of being in the class L (X) is called the Levi-property generated by X . In the case where X is a variety, we s...

Irreducible residuated semilattices and finitely based varieties

This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids (RSs). An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if its finitely sub...