Simple modules and their essential extensions for skew polynomial rings

• Tipo: Artigo em Revista Científica Internacional
• Data: 2019

Autores

Brown, K (Autor) Outra; Paula A.A.B. Carvalho (Autor) FCUP; Matczuk, J (Autor) Outra

Revista

Título: Mathematische Zeitschrift

Vol. 291

Páginas: 877-903

ISSN: 0025-5874

Editora: Springer Nature

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 1 Citação

Classificação Científica

CORDIS: Ciências Físicas > Matemática > Álgebra

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: 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.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 27