An extension of S-artinian rings and modules to a hereditary torsion theory setting

2021/01/25 by Pascual Jara, Jara, Pascual
Mathematics · #13E05 #13E10 #Algebra over a field #Algebraic structures and combinatorial models #Artinian ring #Commutative Algebra (math.AC) #Commutative property #Commutative ring #Discrete mathematics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Multiplicative function #Noetherian #Noetherian ring #Noncommutative ring #Physics #Pure mathematics #Ring (chemistry) #Rings, Modules, and Algebras #Semisimple module #Sigma #Torsion (gastropod) #math.AC #msc:13E05 #msc:13E10

paper · pdf · doi:10.48550/arxiv.2101.10171

published in arXiv (Cornell University) (Cornell University) · 22 pages

arxiv created 2021/01/25 · openalex publication_date 2021/01/25 · arxiv updated 2021/01/26 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/05

Abstract

For any commutative ring A we introduce a generalization of S--artinian rings using a hereditary torsion theory σ instead of a multiplicative closed subset S⊆A. It is proved that if A is a totally σ--artinian ring, then σ must be of finite type, and A is totally σ--noetherian.

Citations

• S-NOETHERIAN RINGS

Related

• An extension of S-noetherian rings and modules
• On torsion-free modules and semi-hereditary rings
• Cotorsion modules relative to a hereditary torsion theory
• Stable torsion theories and the injective hulls of simple modules
• Lattice structure of torsion classes for hereditary artin algebras