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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

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