Modules semicocritical with respect to a torsion theory and their applications

DOI10.1007/BF02764941zbMath0603.16022MaRDI QIDQ1082411

Mark L. Teply

Publication date: 1986

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

endomorphism ringslayerlinkagehereditary torsion theory\(\tau \)- composition series\(\tau \)-primitive ideals\(\tau \)-semicocritical modules\(\tau \)-semicocritical socle seriesascending chain of submodulesDCC on \(\tau \)-closed left idealsindecomposable torsionfree injective module

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Injective modules, self-injective associative rings (16D50) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Modules, bimodules and ideals in associative algebras (16Dxx)

Related Items (9)

The rational Loewy series and nilpotent ideals of endomorphism rings ⋮ When does length equal dimension? ⋮ On the endomorphism ring of a module with relative chain conditions ⋮ Semisiple localizations and v-rings ⋮ A general form of kulikov’s theorem ⋮ Links ore sets, and classical localizations ⋮ Semicocritical modules and their endomorphism rings ⋮ Neat submodules by relative height ⋮ On classical artinian localizations

Cites Work

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• On the endomorphism ring of a module Noetherian with respect to a torsion theory
• The endomorphism ring of a Delta-module over a right Noetherian ring
• The descending chain condition relative to a torsion theory
• Elements of noncommutative arithmetic. I
• Torisonfree injective modules
• α-Injectives and the semicritical socle series
• Semiartinian modules relative to a torsion theory
• Finite σ-length and σ-artinian rings
• Injective Modules and Injective Quotient Rings
• On the structure of indecomposable injective modules¹
• Injective modules with both ascending and descending chain conditions on annihilators
• Rings having a composition series with respect to a torsion theory
• Ideal invariance and localization

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