A Note on Right Full $k$-Ideals of Seminearrings (Journal of Informatics and Mathematical Sciences, 2012)
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