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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Fuzzy Quasi-ideals and Fuzzy Bi-ideals in Semirings
verfasst von : Javed Ahsan, John N. Mordeson, Mohammad Shabir
Erschienen in: Fuzzy Semirings with Applications to Automata Theory
Verlag: Springer Berlin Heidelberg
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The object of this chapter is to study fuzzy quasi-ideals and fuzzy bi-ideals and Section 1 provides a study of these ideals. Section 2 presents various characterizations of regular semirings involving these fuzzy ideals. In Section 3, we examine and characterize regular and intra regular semirings in this context. Section 4 provides a study of fuzzy
k
-quasi-ideals and fuzzy
k
-bi-ideals of semirings and Section 5 contains characterizations of
k
-regular semirings by the ideals studied in Section 4. Section 6 contains characterizations of
k
-intra regular semirings by the ideals examined in the preceding section.
Throughout this chapter
R
will denote a semiring with zero.