N(A)-ternary semigroups

African Journal of Mathematics and Computer Science Research

D. Madhusudhana Rao¹ 

关键词: Pseudo symmetric ideal;    semipseudo symmetric ideal;    prime ideal;    semiprime ideal;    completely prime ideal;    completely semiprime ideal;    semisimple element;    A-potent element;    A-potent Γ    -ideal;    A-divisor;    N(A)- ternary semigroup.;   

DOI  :  10.5897/AJMCSR2013.0470

学科分类：计算机科学（综合）

来源: Academic Journals

【 摘 要 】

In this paper, the terms, ‘A-potent’, ‘left A-divisor’, ‘right A-divisor’, ‘A-divisor’ elements, ‘N(A)-ternary semigroup’ for an ideal A of a ternary semigroup are introduced. If A is an ideal of a ternary semigroup T then it is proved that (1)(2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N2(A). It is also proved that if A is an ideal of a ternary semigroup such that N0(A) = A then A is a completely semiprime ideal. Further it is proved that if A is an ideal of ternary semigroup T then R(A), the divisor radical of A, is the union of all A-divisor ideals in T. In a N(A)- ternary semigroup it is proved that R(A) = N1(A). If A is a semipseudo symmetric ideal of a ternary semigroup T then it is proved that S is an N(A)- ternary semigroup iff R(A) = N0(A). It is also proved that if M is a maximal ideal of a ternary semigroup T containing a pseudo symmetric ideal A then M contains all A-potent elements in T or T\M is singleton which is A-potent.

【 授权许可】

CC BY