Rough Interior Ideals and Rough Quasi-Ideals in Approximation Spaces of Semigroups under Preorder and Compatible Relations
Keywords:Rough interior ideal, Rough quasi-ideal, Approximation space, Semigroup, Preorder and compatible relation
In this paper, a rough interior ideal and a rough quasi-ideal in an approximation space of a semigroup under a preorder and compatible relation are proposed. As introduced above, corresponding examples are presented. Next, we provide a sufficient condition for the rough interior ideal (resp., rough quasi-ideal). Finally, we give a necessary and sufficient condition for a homomorphic image of the rough interior ideal (resp., rough quasi-ideal).
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