Prime submodules of regular modules over commutative rings
M Ershad, N Amiri - Arabian Journal for Science and Engineering, 2011 - Springer
M Ershad, N Amiri
Arabian Journal for Science and Engineering, 2011•SpringerWe 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.
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.
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.
Springer
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