L2-PRIME AND DIMENSIONAL MODULES

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International Electronic Journal of Algebra
Volume:7 Issue:7
L2-PRIME AND DIMENSIONAL MODULES

L2-PRIME AND DIMENSIONAL MODULES

Authors : M R Vedadi

Pages : 47-58

View : 19 | Download : 8

Publication Date : 2010-06-01

Article Type : Research Paper

Abstract :We introduce a map κ that generalizes Krull and Noetherian dimensions. If MR finitely generates all fully invariant submodules and has acc on them, there are only a finite number of minimal L2-prime submodules Piinsert ignore into journalissuearticles values(1 ≤ i ≤ n); and when defined, κinsert ignore into journalissuearticles values(M); = κinsert ignore into journalissuearticles values(M/Pj ); for some j. Here, each M/Pi is a prime R-module, and in particular, M has finite length if every irreducible prime submodule of M is maximal. Quasi-projective L2-prime Rmodule with non-zero socle are investigated and some applications are then given when κinsert ignore into journalissuearticles values(M); means the Krull dimension or the injective dimension.
Keywords : dimension map, hereditary ring, Krull dimension, L2 Noetherian, L2 prime submodule

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