On fuzzy annihilators and primitive fuzzy ideals of a ring

HM Imdadul  Hoque; Helen K.  Saikia

doi:10.5269/bspm.63718

HM Imdadul Hoque Gauhati University
Helen K. Saikia

Abstract

In this paper our attempt is to study the concept like Noetherian quotient in fuzzy setting. If µ and σ are fuzzy ideals of a ring R, then we define, (µ : σ) = ∨{η|ησ ⊆ µ} and it is proved that (µ : σ) is a fuzzy ideal of R. Using this notion annihilator of fuzzy subset of a ring is defined and we introduce the notion of fuzzy primitive ideal via fuzzy Noetherian quotient. Some results on fuzzy primitive ideal and various properties of fuzzy annihilators have been established.

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