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Modules with finitely many submodules

Akbari, S ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1142/S1005386716000444
  3. Publisher: World Scientific Publishing Co. Pte Ltd , 2016
  4. Abstract:
  5. In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module
  6. Keywords:
  7. Direct sum ; Module ; Submodule
  8. Source: Algebra Colloquium ; Volume 23, Issue 3 , 2016 , Pages 463-468 ; 10053867 (ISSN)
  9. URL: http://www.worldscientific.com/doi/abs/10.1142/S1005386716000444