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.
|Number of pages||5|
|Journal||Comptes Rendus Mathematique|
|State||Published - 1 Jan 2017|
Bibliographical noteFunding Information:
The second author has been partially supported by NSERC Discovery Grant 250217-2012.
© 2016 Académie des sciences
ASJC Scopus subject areas
- Mathematics (all)