Abstract
Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.
Original language | English |
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Pages (from-to) | 405-422 |
Number of pages | 18 |
Journal | Beitrage zur Algebra und Geometrie |
Volume | 46 |
Issue number | 2 |
Publication status | Published - 2005 |
Keywords
- Cancellation ideal
- Meet-principal ideal
- Multiplication module
- Residual submodule
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology