Structure of P-Prime and P-Semiprime IdealsinTernary Smearing

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Year:
2015
Type of Publication:
Article
Keywords:
P-C-System, P-D-System, P-M-System, P-NSystem, Completely P-Prime, P-Prime, Completely PSemiprime and P-Semiprime
Authors:
D. Madhusudhana Rao; G. Srinivasa Rao
Journal:
IJISM
Volume:
3
Number:
1
Pages:
24-31
Month:
Jan.-Feb.
ISSN:
2347-9051
Abstract:
In this paper we study the structure of Completely P-prime, P-prime, Completely P-semiprime and P-semiprime and small P-prime ideals in ternary semirings and characterize those ideals in ternary semirings. It is proved that (1) an ideal A of a ternary semiring T is completelyP-prime if and only if T\A is either P-c-system of T or empty, (2)An ideal A of a ternary semiring T is completely P-semiprime if and only if T\A is a P-d-system of T or empty, (3) an ideal A of a ternary semiring T is a P-prime ideal of T if and only if T\A is an P-m-system of T or empty and (4) an ideal Q of a ternary semigroup T is a P-semiprime ideal if and only if T\Q is aP-n-system of T or empty. Mathematical Subject Classification: 16Y30, 16Y99.

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