Base non finie de variétés. (French) Zbl 0572.20041

Irastorza, Christine

Theoretical aspects of computer science, 2nd ann. Symp., Saarbrücken/Ger. 1985, Lect. Notes Comput. Sci. 182, 180-186 (1985).

[For the entire collection see Zbl 0561.00020.]
Semidirect products of varieties of monoids are considered. It is shown that the variety \(J_ 1*({\mathbb{Z}}_ 2)\) has no finite equational base. Here \(J_ 1\) and \(({\mathbb{Z}}_ 2)\) are the varieties of monoids defined by the identities \(x^ 2=x\), \(xy=yx\) and \(x^ 2=1\), \(xy=yx\), respectively.

Reviewer: T.J.Harju

MSC:

20M07	Varieties and pseudovarieties of semigroups
08B05	Equational logic, Mal’tsev conditions
20M35	Semigroups in automata theory, linguistics, etc.
68Q70	Algebraic theory of languages and automata

Keywords:

Semidirect products of varieties of monoids; equational base

Citations:

Zbl 0561.00020