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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.
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 $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.
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.
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.
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:
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 $I=I^2$.