Abstract
In this paper, we study rings whose principal right ideals are left pure. Also we shall introduce the concept of a fuzzy bi-ideal in a ring, and give some properties of such fuzzy ideals. We also give a characterization of whose principal right ideal are left pure, fuzzy duo ring in terms of fuzzy deals.
Highlights
Many authors have studied the theory of fuzzy rings(for example [2]and [4])
In this paper we study rings whose principal right ideal are left pure, we call such rings PILP-rings
We introduce the concepts of a fuzzy bi-ideal in a ring, and give another characterization of a ring PILPrings
Summary
Many authors have studied the theory of fuzzy rings(for example [2]and [4]). A characterization of a regular ring by fuzzy ideals due to Gupta and Kantroo [2] is very interesting. 2- PILP-Rings: Following [1], an ideal I of a ring R is said to be a left (right) pure if for every a I, there exists b I such that a = ba(a=ab). Theorem 2-3: Let R be a right PILP –ring and abelian ring with (a) =0. Since R is PILP –ring, aR is a left pure ideal and there exists b aR such that a = ba =axa , for some x R.
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