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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Author: Jonathan S. Golan
Journal: Proc. Amer. Math. Soc. 81 (1981), 377-381
MSC: Primary 16A63; Secondary 06D20
DOI: https://doi.org/10.1090/S0002-9939-1981-0597644-1
MathSciNet review: 597644
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0597644-1
Keywords: $ H$-ring, torsion theory, simple module, jansian torsion theory, homological independence, Stone lattice
Article copyright: © Copyright 1981 American Mathematical Society