L2-PRIME AND DIMENSIONAL MODULES
L2-PRIME AND DIMENSIONAL MODULES
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.
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- Department of Mathematical Sciences Isfahan University of Technology Isfahan, 84156-83111, Iran e-mail: mrvedadi@cc.iut.ac.ir
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI