• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.679-687
• /
• 2005

In this paper we shall give a new definition for a quasi-power module P(M) and discuss some properties for P(M). The quasi-power module P(M) is a direct sum of invertible quasi-submodules C(H)'s of P(M) and then the quasi-submodule C(H) is also a direct sum of strongly cyclic quasi-submodules of C(H). When M is a quasi-perfect right R-module, we shall see that the quasi-power module P(M) is invertible.

• East Asian mathematical journal
• /
• v.16 no.1
• /
• pp.33-48
• /
• 2000

In this paper, for any ring R with an identity, in order to study prime ideals of the endomorphism ring $End_R$(M) of left R-module $_RM$, meet-prime submodules, prime radical, sum-prime submodules and the prime socle of a module are defined. Some relations of the prime radical, the prime socle of a module and the prime radical of the endomorphism ring of a module are investigated. It is revealed that meet-prime(or sum-prime) modules and semi-meet-prime(or semi-sum-prime) modules have their prime, semi-prime endomorphism rings, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.149-155
• /
• 2005

The notion of U-exact sequence (or quasi-exact sequence) of modules was introduced by Davvaz and Parnian-Garamaleky as a generalization of exact sequences. In this paper, we prove further results about quasi-exact sequences. In particular, we give a generalization of Schanuel's Lemma. Also we obtain some relation-ship between quasi-exact sequences and superfluous (or essential) submodules.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.121-131
• /
• 2005

This paper is motivated by the results in [6]. We study some properties of strongly irreducible submodules of a module. In fact, our objective is to investigate strongly irreducible modules and to examine in particular when sub modules of a module are strongly irreducible. For example, we show that prime submodules of a multiplication module are strongly irreducible, and a characterization is given of a multiplication module over a Noetherian ring which contain a non-prime strongly irreducible submodule.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.613-619
• /
• 2014

It is well known that a direct sum of CLS-modules is not, in general, a CLS-module. It is proved that if $M=M_1{\oplus}M_2$, where $M_1$ and $M_2$ are CLS-modules such that $M_1$ and $M_2$ are relatively ojective (or $M_1$ is $M_2$-ejective), then M is a CLS-module and some known results are generalized.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.553-563
• /
• 2017

Different topological dimensions related to the pseudo-prime spectrum of topological modules are studied. An example of topological modules is introduced. Also, we give a result about Noetherianness of the pseudo-prime spectrum of topological modules.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.649-657
• /
• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.617-629
• /
• 2008

In this paper, the authors have found an equivalent condition of the endomorphism ring End(M) of a projective module M being von Neumann regular(Theorem 1.14) and found an equivalent condition of any associative ring R being von Neumann regular (Theorem 1.13).

• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.51-58
• /
• 2009

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.

• Honam Mathematical Journal
• /
• v.29 no.3
• /
• pp.351-366
• /
• 2007

Let R be a commutative ring and let M be an R-module. Let X = Spec(M) be the prime spectrum of M with Zariski topology. Our main purpose in this paper is to specify the topological dimensions of X, where X is a Noetherian topological space, and compare them with those of topological dimensions of $Supp_{R}$(M). Also we will give a characterization for the irreducibility of X and we obtain some related results.