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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Decompositions of finitely generated modules


Author: Thomas S. Shores
Journal: Proc. Amer. Math. Soc. 30 (1971), 445-450
MSC: Primary 13.40
MathSciNet review: 0281708
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Abstract: A commutative ring with unit is called a d-ring if every finitely generated Loewy module is a direct sum of cyclic submodules. It is shown that every d-ring is a T-ring, i.e., Loewy modules over such rings satisfy a primary decomposition theorem. Some applications of this result are given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281708-X
PII: S 0002-9939(1971)0281708-X
Keywords: Loewy module, primary decomposition, torsion module, finitely generated module, Noetherian Lowey module, T-ring, Loewy series, structure theory for modules
Article copyright: © Copyright 1971 American Mathematical Society