Maximal non-affine reducts of simple affine algebras. (English) Zbl 0836.08002
Let the finite set \(A\) carry a vector space structure \(V\), and let \(F\) be a set of polynomial operations of the algebra obtained by regarding \(V\) as a module over its own endomorphism ring. The “semi-affine” algebra \((A,F)\) may or may not be “affine”, i.e. polynomially equivalent to an algebra on \(A\) obtained by regarding \(V\) as a module over some subring of its endomorphism ring. The present paper is devoted to this distinction; in particular, a necessary and sufficient condition is given for simple semi-affine algebras to be affine. Applications are given to previous work of the author [J. Algebra 151, No. 2, 408-424 (1992; Zbl 0770.08001)].
Reviewer: M.Armbrust (Köln)
MSC:
| 08A05 | Structure theory of algebraic structures |
| 08A40 | Operations and polynomials in algebraic structures, primal algebras |
Citations:
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