Algebras of length one

2021/08/09 by Markova, O. V., Martínez, C., Rodrigues, R. L.
#15A03 #17A01 #17A05 #17A60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2108.04109

Abstract

If \A is an algebra over a field \F and \s is a generating set of \A, the length of \s indicates the maximal length needed to express an arbitrary element of \A as a linear combination of words in the elements of \s. The length of an algebra \A is defined as the maximum of lengths of its generating sets. In this paper (not necessarily associative) algebras, over fields of arbitrary characteristic, having length equal to 1 are determined.

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