In our recent work, we introduced a generalization of the prime ideal factorization in
Dedekind domains for submodules of finitely generated modules over Noetherian rings. In …

A prime (left) Goldie semiprincipal left ideal ring is the endomorphism ring $ E (F, A) $ of a
free module $ A $, of finite rank, over a (left) Ore domain $ F $. We examine the uniqueness …

In [2] we introduced a concept of a Macaulay module over a right noetherian ring by saying
that all associated primes of the module have the same codimension. That is to say that a …

We prove that B+ Ann M= Ann (M/MB) for every finitely generated right module M over a
strongly regular ring A and every ideal B of the ring A. All rings are assumed to be …

A module M is said to be wealdy-injective if and only if for every finitely generated
submodule N of the injective hull E (M) of M there exists a submodule X of E (M), isomorphic …

Characteristic submodules of injective modules over strongly prime rings Page 1 DOI
10.1515/dma-2014-0022 Discrete Math. Appl. 2014; 24 (4):253–256 Askar A. Tuganbaev …

A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …

Let R be an associative ring and M a unitary left R-module. An R-module M is said to be
uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum …

The main result of this thesis is a completely different proof via localization, of the following
theorem due to Bruno J. Muller and Surjeet Singh: For any P-tame uniform module M over a …

Let R be a commutative ring with identity and M be a finitely generated R-module. Let I (M)
be the first nonzero Fitting ideal of M and T (M) be the torsion submodule of M. Then, I (M)⊆ …