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Sarala, Y.
- Semipseudo Symmetric Ideals in Partially Ordered Ternary Semigroups
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International Journal of Innovative Research and Development, Vol 3, No 4 (2014), Pagination:Abstract
In this paper the terms pseudo symmetric ideals, semipseudo symmetric ideals of po ternary semigroups. It is proved that every pseudo symmetric ideal of po ternary semigroup is a semipseudo symmetric ideal. It is also proved that every semiprime ideal P minimal relative to containing a semipseudo symmetric ideal A of a po ternary semigroup is completely semiprime. If A is a semipseudo symmetric ideal of a po ternary semigroup T. Then (1) A1= the intersection of all completely prime ideals of T containing A. 2) = the intersection of all minimal completely prime ideals of T containing A. 3) = the minimal completely semiprime ideal of T relative to containing A.4) for some odd natural number n}5) = the intersection of all prime ideals of T containing A.6) = the intersection of all minimal prime ideals of T containing A.7) = the minimal semiprime ideals of relative to containing A.8) for some odd natural number n } are equivalent. If A is an ideal in a po ternary semigroup then it is proved that (1) A is completely semiprime, A is semiprime and pseudo symmetric. A is semiprime and semipseudo symmetric are equivalent and (2) A is completely prime; A is prime and pseudo symmetric. A is prime and semipseudo symmetric are also equivalent. If M is maximal ideal of a po ternary semigroup T with then it is proved that M is completely prime, M is completely semiprime, M is pseudo symmetric and M is semipseudo symmetric are equivalent.