On quinary semiring and properties of its special subsets

Tuhfatul  Janan

doi:10.20956/j.v21i1.35615

Authors

Tuhfatul Janan Institut Ahmad Dahlan Probolinggo

DOI:

https://doi.org/10.20956/j.v21i1.35615

Keywords:

prime ideal, completely semiprime ideal, insertion property, quinary semiring

Abstract

In this research, we will discuss about quinary semiring and properties of its special subsets. This concept is a generalization of ternary semiring. If ternary semiring only involves 3 elements in multiplication operation, then in quinary semiring there are 5 elements involved. The method in this research is a literature study on articles in international journals. In this research, some definitions and properties of quinary semiring and some ideals are given, such as prime ideal, completely semiprime ideal, ideal which has insertion property, and prime radical. In addition, special subsets of quinary semiring are defined by and . Next, we give some properties of these special subsets.

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