• 대한수학회논문집
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• 제3권2호
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• pp.125-131
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• 1988

• 대한수학회논문집
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• 제19권3호
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• pp.427-433
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• 2004

Conditions for a $\Gamma$-near-ring to be commutative are investigated.

• 대한수학회보
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• 제46권6호
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• 한국수학사학회지
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• 제10권2호
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• pp.24-29
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• 1997

Derivation은 Lie group, Lie ring 그리고 Lie Algebra에서 정의되어 사용되며 발전하였으며 ring에서 일반화 되었다. 역시 prime ring에서 연구되어지는 derivation의 성질들은 prime near-ring에서 일반화 시키려고 하고 있다. 1957년 E. Posner는 prime ring에서 두 개의 derivation의 곱(함수합성)이 derivation이면 이들중 하나의 derivation이 0임을 밝혔다. 본 논문에서는 prime ring에서 derivation이 연구된 역사적인 배경을 소개하고 몇가지 성질을 찾는다. 즉, D. F를 prime ring R의 derivation들이라 할 때 정수 $n{\ge}1$에 대하여 $DF^n$=0이면 D=0이거나 또는 $F^{3n-1}$=0이고, $D^nF$=0이면 $D^{9n-7}$=0 이거나 또는 $F^2$=0 이다.

• 대한수학회논문집
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• 제27권3호
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• pp.483-488
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• 2012

In this paper we introduce the notion of P-strongly regular near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completely semiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) $Na$ + P is an ideal of N for any $a{\in}N$. (ii) Every P-prime ideal of N containing P is maximal. (iii) Every ideal I of N fulfills I + P = $I^2$ + P.

• 대한수학회보
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• 제35권3호
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• pp.455-464
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• 1998

In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

• Kyungpook Mathematical Journal
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• 제19권2호
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• pp.205-211
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• 1979

In this paper we continue the study of formation radical (F-radical) classes initiated in [3]. Hereditary and stronger properties of F-radical classes are discussed by giving construction for lower hereditary, lower stronger and lower strongly hereditary F-radical classes containing a given class M. It is shown that the Baer F-radical B is the lower strongly hereditary F-radical class containing the class of all nilpotent ideals and it is the upper radical class with $\{(I,\;N){\mid}N{\in}C,\;N\;is\;prime\}{\subset}SB$ where SB denotes the semisimple F-radical class of B and C is an arbitrary but fixed class of homomorphically closed near-rings. The existence of a largest F-radical class contained in a given class is examined using the concept of complementary F-radical introduced by Scott [5].

• 대한수학회논문집
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• 제24권2호
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• pp.161-169
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• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.