http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ON STRONGLY REGULAR NEAR-SUBTRACTION SEMIGROUPS
Dheena, P.,Kumar, G. Satheesh Korean Mathematical Society 2007 대한수학회논문집 Vol.22 No.3
In this paper we introduce the notion of strongly regular near-subtraction semigroups (right). We have shown that a near-subtraction semigroup X is strongly regular if and only if it is regular and without non zero nilpotent elements. We have also shown that in a strongly regular near-subtraction semigroup X, the following holds: (i) Xa is an ideal for every a $\in$ X (ii) If P is a prime ideal of X, then there exists no proper k-ideal M such that P $\subset$ M (iii) Every ideal I of X fulfills $I=I^2$.
Dheena, P.,Jenila, C. Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.3
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.
WEAKLY PRIME LEFT IDEALS IN NEAR-SUBTRACTION SEMIGROUPS
Dheena, P.,Kumar, G. Satheesh Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.3
In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.
A GENERALIZED IDEAL BASED-ZERO DIVISOR GRAPHS OF NEAR-RINGS
Dheena, Patchirajulu,Elavarasan, Balasubramanian Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
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.
FUZZY 2-(0-OR 1-)PRIME IDEALS IN SEMIRINGS
Dheena, P.,Coumaressane, S. Korean Mathematical Society 2006 대한수학회보 Vol.43 No.3
In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $m_2-system$ in R.
TOPOLOGICAL CONDITIONS OF NI NEAR-RINGS
Dheena, P.,Jenila, C. Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.4
In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.
AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS
Dheena, Patchirajulu,Elavarasan, Balasubramanian Korean Mathematical Society 2009 대한수학회보 Vol.46 No.6
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).
On Comaximal Graphs of Near-rings
Dheena, Patchirajulu,Elavarasan, Balasubramanian Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.2
Let N be a zero-symmetric near-ring with identity and let ${\Gamma}(N)$ be a graph with vertices as elements of N, where two different vertices a and b are adjacent if and only if <a> + <b> = N, where <x> is the ideal of N generated by x. Let ${\Gamma}_1(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set {n ${\in}$ N : <n> = N} and ${\Gamma}_2(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set $N{\backslash}{\upsilon}({\Gamma}_1(N))$, where ${\upsilon}(G)$ is the set of all vertices of a graph G. In this paper, we completely characterize the diameter of the subgraph ${\Gamma}_2(N)$ of ${\Gamma}(N)$. In addition, it is shown that for any near-ring, ${\Gamma}_2(N){\backslash}M(N)$ is a complete bipartite graph if and only if the number of maximal ideals of N is 2, where M(N) is the intersection of all maximal ideals of N and ${\Gamma}_2(N){\backslash}M(N)$ is the graph obtained by removing the elements of the set M(N) from the vertices set of the graph ${\Gamma}_2(N)$.
Fuzzy 2-(0- or 1-)prime ideals in semirings
P. Dheena,S. Coumaressane 대한수학회 2006 대한수학회보 Vol.43 No.3
In this paper three dierent ypes of fuzzy prime idealsare introduced. Condition is obtained for a fuzzy 2-prime ideal willhave two elements in its range. It has been shown thatA is fuzzy2-prime ideal of the semiringR if and only if 1 A is a fuzzym2-system inR:
An ideal-based zero-divisor graph of 2-primal near-rings
Patchirajulu Dheena,Balasubramanian Elavarasan 대한수학회 2009 대한수학회보 Vol.46 No.6
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 Γ_(I) (R) with respect to the completely semiprime ideal I of N. We show that Γ_(P)(R), where 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 Γ_(P)(R). 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 Γ_(I) (R) with respect to the completely semiprime ideal I of N. We show that Γ_(P)(R), where 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 Γ_(P)(R).