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- Title
Prime Submodules of Regular Modules Over Commutative Rings.
- Authors
Ershad, M.; Amiri, N.
- Abstract
We investigate prime submodules of regular modules. In particular, we shall see that every proper submodule of a regular module M over an integral domain is prime. Although (von Neumann) regular rings are zero dimensional (primes ideals are maximal), it is not true for regular modules in general. We show that cyclic regular module are zero dimensional. Furthermore, it is proved that for a regular module every proper submodule is a radical submodule.
- Subjects
COMMUTATIVE rings; INTEGRAL domains; MODULES (Algebra); VON Neumann regular rings; SUBMODULAR functions; RING theory
- Publication
Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ), 2011, Vol 36, Issue 6, p963
- ISSN
2193-567X
- Publication type
Article
- DOI
10.1007/s13369-011-0087-z