On Uniformly Strongly Prime $\Gamma$-Semihyperring
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Authors: J. J. PATIL AND K. F. PAWAR
DOI: 10.46793/KgJMat2401.079P
Abstract:
The Γ-semihyperring is a generalization of the concepts of a semiring, a semihyperring and a Γ-semiring. The concepts of uniformly strongly (weak) prime Γ-semihyperring and essential extension for the Γ-semihyperring are introduced and studied some important properties in this respect. It is proved that any essential extension of a uniformly strongly prime Γ-semihyperring is a uniformly weak prime Γ-semihyperring. Also strongly prime radical of a Γ-semihyperring is introduced and its characterization is made with the help of a super sp-system. A necessary and sufficient condition for a ideal of Γ-semihyperring to be a right strongly prime ideal is provided with the help of sp-system and super sp-system.
Keywords:
Prime Γ-semihyperring, uniformly strongly prime Γ-semihyperring, super sp-system.
References:
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