Abstract
The purpose of this paper is to present some characterizations of almost fuzzy prime ideals and sub modules; and to introduce certain innovative fuzzy prime ideals and sub modules respectively. Moreover, every fuzzy ideal in R is an almost prime ideal for a quasi-local ring \( (R, M) \) with \( M^{2} = 0 \). Moreover, prime sub module µN in a finitely generated multiplication R − module M and fuzzy prime ideal \( I_{\mu } \) in R have been constructed.
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