Simple modules and their essential extensions for skew polynomial rings

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Brown, K (Author) Other; Paula A.A.B. Carvalho (Author) FCUP; Matczuk, J (Author) Other

Journal

Title: Mathematische Zeitschrift

Vol. 291

Pages: 877-903

ISSN: 0025-5874

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Scientific classification

CORDIS: Physical sciences > Mathematics > Algebra

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00P-J22

DOI: 10.1007/s00209-018-2128-8

Abstract (EN): Let R be a commutative Noetherian ring and an automorphism of R. This paper addresses the question: when does the skew polynomial ring S=R[;] satisfy the property (), that for every simple S-module V the injective hull ES(V) of V has all its finitely generated submodules Artinian. The question is largely reduced to the special case where S is primitive, for which necessary and sufficient conditions are found, which however do not between them cover all possibilities. Nevertheless a complete characterisation is found when R is an affine algebra over a field k and is a k-algebra automorphismin this case () holds if and only if all simple S-modules are finite dimensional over k. This leads to a discussion, involving close study of some families of examples, of when this latter condition holds for affine k-algebras S=R[;]. The paper ends with a number of open questions.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27