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- Title
A Note on Comultiplication Modules.
- Authors
Wang, Yongduo; Liu, Yang
- Abstract
Let R be a commutative ring with identity. An R-module M is said to be a comultiplication module if for every submodule N of M, there exists an ideal I of R such that N=(0:M I). In this paper, we show: (1) If M is a comultiplication module and N is a copure submodule of M, then M/N is a comultiplication module. (2) If M is a comultiplication module satisfying the DAC and N ≤ M, then N ≤e M if and only if there exists I ≪ R such that N=(0:M I). (3) If M is a comultiplication module satisfying the DAC, then M is finitely cogenerated. Finally, we give a partial answer to a question posed by Ansari-Toroghy and Farshadifar.
- Subjects
MULTIPLICATION; MODULES (Algebra); APPLIED mathematics; FINITE geometries; FARSHADIFAR, F.; ANSARI-Toroghy, H.
- Publication
Algebra Colloquium, 2014, Vol 21, Issue 1, p147
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386714000108