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On completely prime and completely semi-prime ideals in \(\Gamma\)-near-rings. (English) Zbl 1223.16023

Summary: We consider the algebraic system \(\Gamma\)-near-rings that was introduced by Satyanarayana. “\(\Gamma\)-near-ring” is a more generalized system than both near-ring and gamma ring. The aim of this short paper is to study and generalize some important results related to the concepts: completely prime and completely semi-prime ideals, in \(\Gamma\)-near-rings. We include examples whenever necessary.

MSC:

16Y99 Generalizations
16D25 Ideals in associative algebras
16Y30 Near-rings
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