• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.455-465
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• 2020

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.357-362
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• 2005

In this paper, we introduce a new notion which we call a generalized weakly ideal. We also investigate characterizations of strongly regular rings with the condition that every maximal left ideal is a generalized weakly ideal. It is proved that R is a strongly regular ring if and only if R is a left GP-V-ring whose every maximal left (right) ideal is a generalized weakly ideal. Furthermore, if R is a left SGPF ring, and every maximal left (right) ideal is a generalized weakly ideal, it is shown that R/J(R) is strongly regular. Several known results are improved and extended.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.225-229
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• 2013

According to the paper in [3], the kernel of an ordered semigroup S is a completely regular subsemigroup of S. In this note we show that the kernel of an ordered semigroup S is not a completely regular subsemigroup of S, in general.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.112-117
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• 2007

The aim of this paper is to characterise regular duo ring R by using the concept of intuitionistic fuzzy left(right,hi,quasi) ideals of R.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.95-100
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• 2006

In this paper we give some new characterizations of the intra-regular ordered semigroups in terms of bi-ideals and quasi-ideals, bi-ideals and left ideals, bi-ideals and right ideals of ordered semigroups.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.645-658
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• 2008

In this paper, left-regular maps on d-algebras are defined. These mappings show behaviors reminiscent of homomorphisms on d-algebras which have been studied elsewhere. In particular for these mappings kernels, annihilators and co-annihilators are defined and some of their properties are investigated, especially in the setting of positive implicative d-algebras.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.561-573
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• 2015

The aim of this paper is to introduce the notion of left-right (resp. right-left) symmetric bi-derivation of BCH-algebras and some related properties are investigated.

• East Asian mathematical journal
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• v.26 no.3
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• pp.397-401
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• 2010

We investigate some properties of strongly reduced near-rings and left regular near-rings, also show that a strongly reduced near-ring is reduced. Next, we will characterize that reducibility, strong reducibility and left regularity in near-rings.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.569-596
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• 2014

In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzied algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy subsystems of ordered semigroups namely (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (${\in},{\in}{\vee}\bar{q}_k$)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

• East Asian mathematical journal
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• v.25 no.4
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• pp.433-440
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• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.