Multiplication modules over non-commutative rings
Journal Article
·
· Sbornik. Mathematics
- Moscow Power Engineering Institute, Moscow (Russian Federation)
It is proved that each submodule of a multiplication module over a regular ring is a multiplicative module. If A is a ring with commutative multiplication of right ideals, then each projective right ideal is a multiplicative module, and a finitely generated A-module M is a multiplicative module if and only if all its localizations with respect to maximal right ideals of A are cyclic modules over the corresponding localizations of A. In addition, several known results on multiplication modules over commutative rings are extended to modules over not necessarily commutative rings.
- OSTI ID:
- 21208364
- Journal Information:
- Sbornik. Mathematics, Vol. 194, Issue 12; Other Information: DOI: 10.1070/SM2003v194n12ABEH000788; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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