Homological independence of injective hulls of simple modules over certain noncommutative rings

Jonathan S. Golan

doi:10.1090/S0002-9939-1981-0597644-1

Homological independence of injective hulls of simple modules over certain noncommutative rings

Jonathan S. Golan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study noncommutative rings R having the property that there is no nonzero homomorphism between injective hulls of nonisomorphic simple left R-modules. For rings satisfying the condition that the torsion theory cogenerated by the injective hull of a simple left R -module is always jansian, we characterize this property in terms of the lattice of torsion theories on the category of left R -modules.

Original language	English
Pages (from-to)	377-381
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	81
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1981-0597644-1
State	Published - Mar 1981

Keywords

H-ring
Homological independence
Jansian torsion theory
Simple module
Stone lattice
Torsion theory

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1981-0597644-1

Cite this

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AB - We study noncommutative rings R having the property that there is no nonzero homomorphism between injective hulls of nonisomorphic simple left R-modules. For rings satisfying the condition that the torsion theory cogenerated by the injective hull of a simple left R -module is always jansian, we characterize this property in terms of the lattice of torsion theories on the category of left R -modules.

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KW - Jansian torsion theory

KW - Simple module

KW - Stone lattice

KW - Torsion theory

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Homological independence of injective hulls of simple modules over certain noncommutative rings

Abstract

Keywords

ASJC Scopus subject areas

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