2019
DOI: 10.1007/s11856-019-1937-8
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On polynomials that are not quite an identity on an associative algebra

Abstract: Let f be a polynomial in the free algebra over a field K, and let A be a K-algebra. We denote by SA(f ), AA(f ) and IA(f ), respectively, the 'verbal' subspace, subalgebra, and ideal, in A, generated by the set of all f -values in A. We begin by studying the following problem: if SA(f ) is finite-dimensional, is it true that AA(f ) and IA(f ) are also finite-dimensional? We then consider the dual to this problem for 'marginal' subspaces that are finite-codimensional in A. If f is multilinear, the marginal subs… Show more

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