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A necessary and sufficient condition for a direct sum of modules to be distributive.
- Source :
- Communications in Algebra; 2024, Vol. 52 Issue 2, p900-907, 8p
- Publication Year :
- 2024
-
Abstract
- Let R be an associative ring with unity. A unital left R-module M is said to be distributive if for every submodules S, T and U of M, the equality S ∩ (T + U) = S ∩ T + S ∩ U holds true. In this paper, we give a necessary and sufficient condition for a direct sum of left R-modules to be distributive. This condition is given by the notion of splitting of submodules of the direct sum and the proof uses the notion of orthogonality, where both notions are discussed and revisited. [ABSTRACT FROM AUTHOR]
- Subjects :
- ASSOCIATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 52
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 175363426
- Full Text :
- https://doi.org/10.1080/00927872.2023.2252516