Proceedings of the American Mathematical Society

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



Decomposition of graded modules

Author: Cary Webb
Journal: Proc. Amer. Math. Soc. 94 (1985), 565-571
MSC: Primary 13C05
MathSciNet review: 792261
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Abstract: In this paper, the primary objective is to obtain decomposition theorems for graded modules over the polynomial ring $ k[x]$, where $ k$ denotes a field. There is some overlap with recent work of Höppner and Lenzing. The results obtained include identification of the free, projective, and injective modules. It is proved that a module that is either reduced and locally finite or bounded below is a direct sum of cyclic submodules. Pure submodules are direct summands if they are bounded below. In such case, the pure submodule is itself a direct sum of cyclic submodules. It is also noted that Cohen and Gluck's Stacked Bases Theorem remains true if the modules are graded.

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Keywords: Graded module, direct sum, pure submodule
Article copyright: © Copyright 1985 American Mathematical Society