• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.419-430
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• 2005

In this paper, we introduce the notions of ($\in,\;{\in} V q$)-fuzzy subnear-ring, ($\in,\;{\in} V q$)-fuzzy ideal and ($\in,\;{\in}V q$)-fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such ($\in,\;{\in}V q$)-fuzzy ideals are also obtained.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.523-527
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• 2011

In this paper, We initiate a 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.

• 한국지능시스템학회논문지
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• 제22권3호
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• pp.394-398
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• 2012

Based on the theory of a bipolar fuzzy set, the notion of a bipolar fuzzy subring/ideal of a Near ring is introduced and related properties are investigated. Characterizations of a bipolar fuzzy subnear ring and a bipolar fuzzy ideal in near ring are established. Relations between a bipolar fuzzy ideal and a level cut are discussed. Using bipolar fuzzy ideals, we discuss characterizations of Noetherian Near ring.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.483-488
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• 2007

Given a set ${\Omega}$, the notion of ${\Omega}-fuzzy$ ideals in a near-ring is introduced, and related properties are investigated. Using fuzzy ideals, ${\Omega}-fuzzy$ ideals are described. Conversely, fuzzy ideals are constructed by using ${\Omega}-fuzzy$ ideals.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.31-47
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• 2020

In this paper, we discuss in detail some of the properties of the new kind of (∈, ∈ ∨q)-fuzzy ideals in Near-ring. The concept of (∈, ∈ ∨q^δ₀)-fuzzy ideal of Near-ring is introduced and some of its related properties are investigated.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.603-613
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• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.