Irastorza, Christine 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 Cited in 1 ReviewCited in 6 Documents 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 PDF BibTeX XML OpenURL