• Bulletin of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.511-515
• /
• 2012

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.573-583
• /
• 2005

In this paper, all near-rings R are left near-rings and all representations of R are (right) R-groups. We start with a study of AR, almost AR and AGR rings which are motivated by the works on the Sullivan's Problem [10] and its properties. Next, for any R-group G, we introduce a notion of R-groups with M R-property and investigate their properties and some characterizations of these R-groups. Finally, for the faithful M R-property, we get a commutativity of near-rings and rings.

• Kyungpook Mathematical Journal
• /
• v.50 no.3
• /
• pp.411-417
• /
• 2010

Some characterizations of regular $\Gamma$-rings are described by means of fuzzy ideals. The concepts of fuzzy interior ideals in $\Gamma$-rings and semisimple $\Gamma$-rings are introduced. Some characterizations of semisimple $\Gamma$-rings are investigated by means of fuzzy interior ideals.

• The Pure and Applied Mathematics
• /
• v.14 no.3
• /
• pp.153-159
• /
• 2007

The notion of bi-ideals in near-rings was effectively used to characterize the near-fields. Using this notion, various generalizations of regularity conditions have been studied. In this paper, we generalize further the notion of bi-ideals and introduce the notion of weak bi-ideals in near-rings and obtain various characterizations using the same in left self distributive near-rings.

• Honam Mathematical Journal
• /
• v.31 no.4
• /
• pp.639-644
• /
• 2009

In this paper, we begin with to introduce the concepts of IFP and strong IFP in near-rings and then give some characterizations of IFP in near-rings. Next we derive reversible IFP, and then equivalences of the concepts of strong IFP and strong reversibility. Finally, we obtain some conditions to become strong IFP in right permutable near-rings and strongly reversible near-rings.

• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.389-392
• /
• 2009

The purpose of this note is to improve several known results on GQ-injective rings. We investigate in this paper the von Neumann regularity of left GQ-injective rings. We give an answer a question of Ming in the positive. Actually it is proved that if R is a left GQ-injective ring whose simple singular left R-modules are GP-injective then R is a von Neumann regular ring.

• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• pp.629-633
• /
• 2003

We investigate in this paper rings containing a finitely generated p-injective maximal left ideal. We show that if R is a semiprime ring containing a finitely generated p-injective maximal left ideal, then R is a left p-injective ring. Using this result we are able to give a new characterization of von Neumann regular rings with nonzero socle.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.23-29
• /
• 2019

Rings in which all accessible subrings are ideals are called filial. A ring R is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.397-405
• /
• 2022

In this article we investigate the transfer of multiplication-like properties to homomorphic images, direct products and amalgamated duplication of a ring along an ideal. Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned properties.

• The Pure and Applied Mathematics
• /
• v.30 no.4
• /
• pp.377-395
• /
• 2023

The purpose of this paper is to consider the abstract theory of hypernear rings. In this regard, we derive the isomorphism theorems for hypernear rings as well as Chinese Remainder theorem. Our results can be considered as a generalization for the cases of Krasner hyperrings, near rings and rings.