α-fuzzy ideals and space of prime α-fuzzy ideals in distributive lattices
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In this paper, we introduce the concept of $\alpha$-fuzzy ideals of a distributive lattice. We prove that the set of all $\alpha$-fuzzy ideals of a lattice forms a complete distributive lattice. A set of equivalent conditions are derived for a fuzzy ideal of a lattice to become an $\alpha$-fuzzy ideal. We also topologize the set of all prime $\alpha$-fuzzy ideals of a distributive lattice. Properties of the space also studied. Moreover, a set of equivalent conditions are given the space of all prime $\alpha$-fuzzy ideals of $L$ to become Hausdorff and regular.
Abstract
In this paper, we introduce the concept of $\alpha$-fuzzy ideals of a distributive lattice. We prove that the set of all $\alpha$-fuzzy ideals of a lattice forms a complete distributive lattice. A set of equivalent conditions are derived for a fuzzy ideal of a lattice to become an $\alpha$-fuzzy ideal. We also topologize the set of all prime $\alpha$-fuzzy ideals of a distributive lattice. Properties of the space also studied. Moreover, a set of equivalent conditions are given the space of all prime $\alpha$-fuzzy ideals of $L$ to become Hausdorff and regular.
참고문헌 (15)
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