Papers by Patchirajulu Dheena
Properties of regular weakly divisible near-rings are obtained. We give some characterization of ... more Properties of regular weakly divisible near-rings are obtained. We give some characterization of regular weakly divisible near-rings. We show that if N is a left π-duo weakly divisible near-ring and if K is a left invariant of N, then K is an invariant N-subgroup and it is prime of type 2.
Journal of Mathematical and Computational Science, 2022
In this short note, we introduce the notion of prime ideals in nearring and obtain equivalent con... more In this short note, we introduce the notion of prime ideals in nearring and obtain equivalent conditions for an ideal to be a weakly prime ideal.
Bulletin of the Korean Mathematical Society, 2006
Kyungpook mathematical journal, 2009
Let N be a zero-symmetric near-ring with identity and let Γ(N) be a graph with vertices as elemen... more Let N be a zero-symmetric near-ring with identity and let Γ(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 Γ1(N) be the subgraph of Γ(N) generated by the set {n ∈ N : n = N } and Γ2(N) be the subgraph of Γ(N) generated by the set N \v(Γ1(N)), where v(G) is the set of all vertices of a graph G. In this paper, we completely characterize the diameter of the subgraph Γ2(N) of Γ(N). In addition, it is shown that for any near-ring, Γ2(N)\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 Γ2(N)\M (N) is the graph obtained by removing the elements of the set M (N) from the vertices set of the graph Γ2(N).
Expert Systems with Applications
Decision-making problems often involve a complex decision-making process in which multiple requir... more Decision-making problems often involve a complex decision-making process in which multiple requirements and uncertain conditions have to be taken into consideration simultaneously. We are often required to deal with uncertainty, subjectiveness and imprecise data, which are represented by fuzzy data. In this paper, we consider the ideal solution and the anti-ideal solution and assess each alternative in terms of distance as well as similarity to the ideal solution and the anti-ideal solution. To minimize the error, the normalization of fuzzy data is carefully avoided. To get greater accuracy in ranking fuzzy rating, we use the latest and advanced similarity measure. Distance and similarity measures for fuzzy numbers are used and aggregation is guided by the decision rules in order to construct decision function. Further, OWA operators with maximal entropy are used to aggregate across all criteria and the overall score of each alternative is determined The proposed method is more flex...
We introduce the notion of fuzzy small right ideal, fuzzy small right prime ideal and fuzzy maxim... more We introduce the notion of fuzzy small right ideal, fuzzy small right prime ideal and fuzzy maximal small right ideal in a ring. We obtain necessary and sufficient condition for a fuzzy small right ideal to be fuzzy small prime right ideal. We also show that fuzzy Jacobson radical is the sum of fuzzy small right ideals.
We introduce the notion of fuzzy small right ideal,fuzzy small right prime ideal and fuzzy maxima... more We introduce the notion of fuzzy small right ideal,fuzzy small right prime ideal and fuzzy maximal small right ideal in a ring. We have obtained necessary and su�cient condition for a fuzzy small right ideal to be fuzzy small prime right ideal. We have also shown that fuzzy Jacobson radical is the sum of fuzzy small right ideals.
In this note we remark that Theorem 3.10 given by R. Ezhilarasi and S. Sriram [ibid. 17, No. 4, 8... more In this note we remark that Theorem 3.10 given by R. Ezhilarasi and S. Sriram [ibid. 17, No. 4, 867–875 (2009; Zbl 1191.06008)] appears to be wrong. We give a counterexample for Theorem 3.10. However, we get rid of this problem by altering a condition of the proposed Theorem 3.10 [loc. cit.].
In this paper, we prove, among others, that in right chains, the proper ideals are completely pri... more In this paper, we prove, among others, that in right chains, the proper ideals are completely prime if and only if they are completely semiprime and that the proper right ideals are prime if and only if they are semiprime. Moreover, the proper non-zero idempotent ideals are completely prime.
We introduce the concepts of semi po near-ring and natural po near-ring. We give some characteriz... more We introduce the concepts of semi po near-ring and natural po near-ring. We give some characterization of semi po near-ring and natural po near-ring. We obtain necessary and sufficient condition for a natural po near-ring to be po left strongly regular. We have also shown that (I:S) is a po ideal of a semi po near-ring N as well as natural po near-ring N. We have shown that N is regular if and only if N is natural partial order regular.
We define fuzzy nilpotent ideals and we show that the characteristic function f A is a fuzzy nilp... more We define fuzzy nilpotent ideals and we show that the characteristic function f A is a fuzzy nilpotent ideal of R iff A is a nilpotent ideal of R. We show that a semiring R is regular and subcommutative iff (i) Every fuzzy ideal of R is idempotent and (ii) For every x∈R, f Rx is a fuzzy ideal and for any y∈R, yx=xz for some z∈R. Finally we show that any fuzzy ideal of a strongly regular ring R is a fuzzy maximal ideal iff it is a fuzzy prime ideal.
Uploads
Papers by Patchirajulu Dheena