Abstract
We study (complete) fuzzy ideals on semilattices from the point of view of tensor products of semilattices. We show that the lattice of all complete fuzzy ideals on a semilattice is an extension of tensor product. We define the notion of semicomplete bi-ideals, and show that the lattice of all fuzzy ideals on a distributive lattice is isomorphic to the lattice of all semicomplete bi-ideals. Moreover, we show that the lattice of all (complete) fuzzy ideals on a distributive (algebraic) lattice is distributive.
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