## Base non finie de variétés.(French)Zbl 0572.20041

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

Zbl 0561.00020