Decompositions of universal algebras by idempotent algebras
An algebra in which every subalgebra contains a singleton subalgebra (exactly one singleton subalgebra) is called an algebra with units (resp. a one-unit-algebra). Let K be a class of algebras. The Mal'tsev products \(U_{\dot K}V\), \(V_{\dot K}U\) are studied, where U is a class of one- unit-K-algebras and V is a class of idempotent K-algebras, so as the intersection \(U_{\dot K}V\cap V_{\dot K}U\). The classes K, U, V are assumed to satisfy some natural conditions. Some consequences for semigroups and quasigroups are obtained. Remark of the reviewer. The author obviously doesn't know the corresponding papers of \textit{I. I. Mel'nik} [Issled. Algebr., 32-40 (1969; Zbl 0265.08003); Teor. Polugrupp Prilozh. 3, 59-63 (1974; Zbl 0353.08002)], in which some results of the author were obtained. See also the reviewer's remark in Zbl 0537.08005 on the author's paper in Trans. Am. Math. Soc. 281, 309-321 (1984).
scientific article; zbMATH DE number 3867411
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