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- Title
PRIME CORRESPONDENCE BETWEEN A GRADED SEMIRING R AND ITS IDENTITY COMPONENT R<sub>1</sub>.
- Authors
JOSEPH, ROSY; SHARMA, RAM PARKASH
- Abstract
The generalization of the results of group theory and ring theory to semirings is a very desirable feature in the domain of mathematics. The analogy between rings graded by a finite group G and rings on which G acts as automorphism has been observed by a number of mathematicians. The results of M. Lorenz and D.S. Passman [3], M. Lorenz, S. Montgomery and L.W. Small [4] proved for the rings with finite groups acting on them were extended by M. Cohen and S. Montgomery [1] for the group graded rings. Motivated by the analogy between the rings graded by a finite group G and rings on which G acts as automorphisms, we have derived certain results for a group graded semiring R, its ring of differences RΔ, and the smash product R # K[G]*, where R is a Ksemialgebra over a commutative semiring K in [7]. In this paper, we study some fundamental properties of subtractive, prime ideals of a Group graded semiring R and its identity component R1. We establish the existence of fuzzy ideals of R1 corresponding to the fuzzy ideals of R which enables us to settle many results for fuzzy ideals of R and R1.
- Subjects
SEMIRINGS (Mathematics); RING theory; PRIME ideals; IDEALS (Algebra); MAXIMAL ideals
- Publication
Journal of Combinatorics, Information & System Sciences, 2015, Vol 40, Issue 1-4, p41
- ISSN
0250-9628
- Publication type
Article