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Modules which satisfy the radical formula
(Akademiai Kiado, 2002) Pusat-Yılmaz, Dilek; Smith, Patrick F.
Let R be a commutative ring. Then an R-module M satisfies the radical formula when M = M-1 circle plus M-2 is a direct sum of a submodule M-1 which satisfies the radical formula and a semi-artinian submodule M-2.
Radicals of submodules of free modules
(Marcel Dekker Inc, 1999) Pusat-Yılmaz, Dilek; Smith, Patrick F.
In this paper we describe the radical of a finitely generated submodule N of a Gee module F of finite rank. As a result of this characterization we can obtain the radical of a finitely generated module over a commutative Noetherian ring. Some examples are also given to illustrate the usefulness and practicality of the method presented here.