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- Title
ON MULTIPLICATION fs-MODULES AND DIMENSION SYMMETRY.
- Authors
JAVDANNEZHAD, S. M.; MOUSAVINASAB, S. F.; SHIRALI, N.
- Abstract
In this paper, we first study fs-modules, i.e., modules with finitely many small submodules. We show that every fs-module with finite hollow dimension is Noetherian. Also, we prove that an R-module M with finite Goldie dimension, is an fs-module if and only ifM = M1...M2, where M1 is semisimple and M2 is an fs-module with Soc(M2)M << M. Then, we investigate multiplication fs-modules over commutative rings and we prove that the lattices of R-submodules of M and S-submodules of M are coincide, where S = EndR(M). Consequently, MR and SM have the same Krull (Noetherian, Goldie and hollow) dimension. Further, we prove that for any self-generator multiplication module M, the fs-module as a right R-module and as a left S-module are equivalent.
- Subjects
MULTIPLICATION; MODULES (Algebra); DIMENSION theory (Algebra); COMMUTATIVE rings; LATTICE theory
- Publication
Journal of Mahani Mathematical Research Center, 2023, Vol 12, Issue 2, p363
- ISSN
2251-7952
- Publication type
Article
- DOI
10.22103/jmmr.2023.20103.1324