On the number of generators of an algebra

Uriya A. First; Zinovy Reichstein

doi:10.1016/j.crma.2016.11.015

On the number of generators of an algebra

Research output: Contribution to journal › Article › peer-review

Abstract

A classical theorem of Forster asserts that a finite module M of rank ≤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.

Original language	English
Pages (from-to)	5-9
Number of pages	5
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	1
DOIs	https://doi.org/10.1016/j.crma.2016.11.015
State	Published - 1 Jan 2017
Externally published	Yes

Bibliographical note

Funding Information:
The second author has been partially supported by NSERC Discovery Grant 250217-2012.

Publisher Copyright:
© 2016 Académie des sciences

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2016.11.015

Cite this

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On the number of generators of an algebra

Abstract

Bibliographical note

ASJC Scopus subject areas

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