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Lifting comaximal decomposition
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PRE
AI
DOI：10.1007/s12215-026-01406-w.png)
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Abstract
En 中文
A submodule N of an R-module M is lifting if AnnR(MN) is a lifting ideal of R, i.e., if r(1-r)M subset of N for some r is an element of R, then there exists an idempotent e is an element of R such that (r-e)M subset of N. We show that R is a clean ring if and only if every submodule of any R-module M is lifting. A lifting comaximal decomposition of a submodule N of an R-module M is N=boolean AND i=1nNi, where Ni ' s are lifting submodules of M such that (Ni:M)+(Nj:M)=R, for all i not equal j. If R is a Noetherian ring and M is a finitely generated multiplication R-module, then we show that every proper submodule of M has a unique (up to order) lifting comaximal decomposition. We will also examine lifting submodules from the point of view of the Zariski topology.
Keywords:
Decomposition of a submodule
Lifting ideals
Lifting submodules
Multiplication modules
Clean rings
Zariski topology
Journal
R
IF:
0.9
Papers:
98
Citations:
0