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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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