On Prime and semiprime ideals of \Gamma-semihyperrings
Publish place: The Journal of Algebra and Related Topics، Vol: 9، Issue: 1
Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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JR_JART-9-1_010
تاریخ نمایه سازی: 31 تیر 1403
Abstract:
The \Gamma-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a \Gamma-semiring. In this paper, the notions of completely prime ideals and prime radicals for \Gamma-semihyperring are introduced and studied some important properties accordingly. We also introduced the notions of m-system and complete m-system. Then characterizations of prime ideals and completely prime ideals of \Gamma-semihyperring with the help of m-system and complete m-system has been taken into account. It is our attempt to find a bridge between semiprime (completely semiprime) ideals and prime (completely prime) ideals of a \Gamma-semihyperring.