A Note on Right Full $k$-Ideals of Seminearrings

Nanthaporn Kornthorng, Aiyared Iampan

Abstract


This work extends the idea of $k$-ideals of semirings to seminearrings, the concept of $k$-ideals of seminearrings is introduced and investigated, which is an interesting for seminearrings and some interesting characterizations of $k$-ideals of seminearrings are obtained. Also, we prove that the set of all right full $k$-ideals of an additively inverse seminearring in which addition is commutative forms a complete lattice which is also modular in the same way as of the results of Sen and Adhikari.

Keywords


Semiring; (additively inverse) seminearring; (right full) $k$-ideal; (modular) complete lattice

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DOI: http://dx.doi.org/10.26713%2Fjims.v4i3.90

eISSN 0975-5748; pISSN 0974-875X