Modules with Finite Submodule-Lengths
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2010, Volume 2, Issue 1, Pages 1-16
AbstractIn this paper, the concepts of submodule with finite submodule-length, and module with finite submodule-lengths are introduced. These concepts are generalizations of the concepts of ideal with finite ideal-length and ring with finite ideal-length.
A submodule N of an R-module M is said to have finite submodule length if comp(I) is finite and (M / I M)P , is an Artinian and Noetherian (R / I)P-module, P = P / I , I = (N:M) and P comp(I). An R-module M has finite submodule-lengths if each submodule of M has finite submodule-length. The basic results about these concepts, and some relationships between modules with finite submodule-lengths and other classes of modules are given.
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