L2-PRIME AND DIMENSIONAL MODULES

Year 2010, Volume: 7 Issue: 7, 47 - 58, 01.06.2010

M. R. Vedadi

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 Pi(1 ≤ i ≤ n) and when defined, κ(M) = κ(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 κ(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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• Department of Mathematical Sciences Isfahan University of Technology Isfahan, 84156-83111, Iran e-mail: [e-mail]