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Fuzzy semirings. (English) Zbl 0796.16038
Summary: We initiate the study of fuzzy semirings and fuzzy $A$-semimodules where $A$ is a semiring and $A$-semimodules are representations of $A$. In particular, semirings all of whose ideals are idempotent, called fully idempotent semirings, are investigated in a fuzzy context. It is proved, among other results, that a semiring $A$ is fully idempotent if and only if the lattice of fuzzy ideals of $A$ is distributive, under the sum and product of fuzzy ideals. It is also shown that the set of proper fuzzy prime ideals of a fully idempotent semiring $A$ admits the structure of a topological space, called the fuzzy prime spectrum of $A$.

16D252-sided ideals (associative rings and algebras)
16D10General module theory (associative rings and algebras)
Full Text: DOI
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