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arXiv · 1610.08156

On the number of generators of an algebra

Uriya A. First·Zinovy Reichstein
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Abstract

A classical theorem of Forster asserts that a finite module $M$ of rank $\leq n$ over a Noetherian ring of Krull dimension $d$ can be generated by $n + d$ elements. We prove a generalization of this result, with "module" replaced by "algebra". Here we allow arbitrary finite algebras, not necessarily unital, commutative or associative. Forster's theorem can be recovered as a special case by viewing a module as an algebra where the product of any two elements is $0$.

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Uriya A. First, Zinovy Reichstein. 2016-10-26. On the number of generators of an algebra. https://doi.org/10.1016/j.crma.2016.11.015

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