Main Article Content
In this paper, we introduce the notion of RG-semigroup. We prove that every ring determines an RG-semigroup. We also introduce the notions of RG-ideal of RG-semigroup, and we investigate RG-ideal properties. Moreover, we introduce the notion of a congruence relation on RG-semigroup, and we construct the quotient RG-semigroup. Furthermore, we introduce the notion of RG-semigroup homomorphism and RG-semigroup isomorphism, and we provide some of its properties.
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