On the number of generators of an algebra

Uriya A. First, Zinovy Reichstein

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)5-9
Number of pages5
JournalComptes Rendus Mathematique
Volume355
Issue number1
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes

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

  • Mathematics (all)

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