Ternary \(\Gamma\)-semihyperrings: ideals and ideals extensions. (English) Zbl 1481.16055
Summary: The aim of this research work is to define a new class of multi-algebras that is called ternary \(\Gamma\)-semihyperrings as a generalization of \(\Gamma\)-semihyperrings and semihyperrings. Then, we define and study the concepts of ideals, mutual ideals, spectrum ideals, strong prime ideals and ultra-prime ideals of them. Also, we define a topology on the set of strong prime ideals. Finally, we introduce the concept of ideal extensions and obtain some related results.
Keywords:
ternary \(\Gamma\)-semihyperring; mutual ideal; spectrum ideal; strong prime ideal; ultra-prime; ideal extensionsReferences:
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