Vague prime ideals and vague primary ideals of vague rings

Abstract

A vague binary operation on a set X with respect to [a fuzzy equality on X] x X and [a fuzzy equality on X] is a strong fuzzy function õ with respect to [a fuzzy equality on X] x X on X x X and a fuzzy equality [a fuzzy equality on X]. Moreover, a vague ring with respect to E [subscript H x H] and E [subscriptH] defined in 2007 by Sezer is a 3-tuple [a vague ring] satisfying some certain conditions. Vague ideals and vague prime ideals were defined in 2007 by the same author. In this thesis, we present vague primary ideals and some elementary properties of vague prime ideals, vague primary ideals and their related vague ideals. In addition, we give the sufficient condition of the vague ring of matrices to have no vague prime ideals. Eventually, we give some sufficient conditions which vague prime ideals, vague primary ideals and some related vague ideals are coincide.