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Quasi-affine algebras. (English) Zbl 0573.08003
An algebra \({\mathfrak B}\) is a subreduct of \({\mathfrak A}=(A,F)\) if \({\mathfrak B}\) is a subalgebra of a reduct of \({\mathfrak A}\). \({\mathfrak A}=(A,F)\) is affine if there is an abelian group operation \(+\) on \({\mathfrak A}\) such that \(x- y+z\) is a term function of \({\mathfrak A}\) and every \(f\in F\) is a homomorphism with respect to \(x-y+z\). \({\mathfrak A}\) is quasi-affine if it is a subreduct of an affine algebra. Denote by \({\mathcal A}(\tau)\) or \({\mathcal Q}(\tau)\) the class of all affine or quasi-affine algebras of the type \(\tau\), respectively. Theorem 1 asserts that \({\mathcal Q}(\tau)\) is a quasivariety and Theorem 4 shows that \({\mathcal Q}(\tau)\subseteq {\mathcal A}(\tau)\) but \({\mathcal Q}(\tau)\neq {\mathcal A}(\tau)\) in general. By the author’s words, the paper is a description of how far \({\mathcal Q}(\tau)\) is from \({\mathcal A}(\tau)\).
Reviewer: I.Chajda

MSC:
08A40 Operations and polynomials in algebraic structures, primal algebras
08C15 Quasivarieties
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