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Vietnam Journal of Mathematics 38:3 (2010) 287-298  

On Connes Subgroups and Graded Semirings

Ram Parkash Sharma and Madhu

Abstract. Semirings are studied either in their own right, in an attempt to broaden techniques coming from semigroup theory or generalization of group theory and ring theory or in connection with their applications. For the generalization of ring theoretic results, in the absence of additive inverses, one has to impose some weaker versions of additive inverses on semirings. In [4] Montgomery and Passman introduced Connes subgroup of a group G and related it to the ideal structures of a G-graded ring and its smash product. This paper generalizes the above ring theoretic relation for additively cancellative yoked semirings and computes the Connes subgroup $\Gamma_R$ of a G-graded semiring R in terms of support (R), when R1  is prime.

2000 Mathematics Subject Classification: 16Y60, 16Y99.

Keywords: Connes subgroup, graded semirings, prime ideals, smash products.

 

 

 

 

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