• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.503-509
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• 2017

We in this note consider a generalized ring theoretic property of quasi-commutative rings in relation with powers. We will use the terminology of weakly left quasi-commutative for the class of rings satisfying such property. The properties and examples are basically investigated in the procedure of studying idempotents and nilpotent elements.

• East Asian mathematical journal
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• v.24 no.4
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• pp.377-387
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• 2008

We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.909-917
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• 2001

In this paper we define product between fuzzy ${H_v}-ideals$ of given ${H_v}-rings$. we consider the fundamental relation ${\gamma}^*$ defined on and ${H_v}-ring$ and give some properties of the fundamental relations and fundamental rings with respect to the product of fuzzy ${H_v}-ideals$.

• East Asian mathematical journal
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• v.31 no.5
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• pp.677-684
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• 2015

In [7], it was shown that Euclidean rings R of imaginary quadratic integers admit unitary number systems. In this paper, as an application of the result, we obtain all self similar tiles arising from the unitary number systems of R.

• East Asian mathematical journal
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• v.29 no.3
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• pp.255-258
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• 2013

In this paper, we initiate the study of zero symmetric and constant parts of near-rings, and then apply these to self map near-rings. Next, we investigate that every near-ring can be embedded into some self map near-ring, and every zero symmetric near-ring can be embedded into some zero symmetric self map near-ring.

• East Asian mathematical journal
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• v.33 no.1
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• pp.75-81
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• 2017

It is a well-known fact that a ring R is regular if and only if every left R-modules is flat. In this article we prove that a ring R is strongly regular if and only if every left R-modules is reduced if and only if every left-R modules is quasi-reduced.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.593-601
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• 1996

W. Liu [11] has studied fuzzy ideals of a ring, and many researchers [5,6,7,16] are engaged in extending the concepts. The notion of fuzzy ideals and its properties were applied to various areas: semigroups [8,9,10,13,15], distributive lattices [2], artinian rings [12], BCK-algebras [14], near-rings [1]. In this paper we obtained an exact analogue of fuzzy ideals for near-ring which was discussed in [5, 11].

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.719-731
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• 2007

R is called a right ${\Pi}-coherent$ ring in case every finitely generated torsion less right R-module is finitely presented. In this paper, we define a dimension for rings, called ${\Pi}-coherent$ dimension, which measures how far away a ring is from being ${\Pi}-coherent$. This dimension has nice properties when the ring in question is coherent. In addition, we study some properties of ${\Pi}-coherent$ rings in terms of preenvelopes and precovers.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1311-1322
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• 2008

The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the Four Conjecture proposed by Gerstein.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1103-1112
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• 2018

We study the structure of a generalization of right nilpotent-duo rings in relation with powers of elements. Such a ring property is said to be weakly right nilpotent-duo. We find connections between weakly right nilpotent-duo and weakly right duo rings, in several algebraic situations which have roles in ring theory. We also observe properties of weakly right nilpotent-duo rings in relation with their subrings and extensions.