Maximal ideals in regular rings

Normal Ideals in Regular Rings

Rings with no Maximal Ideals

In this note we give examples of a ring that has no maximal ideals. Recall that, by a Zorn’s lemma argument, a ring with identity has a maximal ideal. Therefore, we need to produce examples of rings without identity. To help motivate our examples, let S be a ring without identity. We may embed S in a ring R with identity so that S is an ideal of R. Notably, set R = Z⊕S, as groups, and where mul...

Intuitionistic Fuzzy Ideals in Intra-regular Rings

The aim of this paper is to characterise intra-regular ring R by using the concept of intuitionistic fuzzy left(right,bi,quasi) ideals of R.

Fuzzy Maximal Ideals of Gamma Near-Rings∗

Fuzzy maximal ideals and complete normal fuzzy ideals in Γ-near-rings are considered, and related properties are investigated.

Complete Ideals in 2-dimensional Regular Local Rings

The objective of these notes is to present a few important results about complete ideals in 2–dimensional regular local rings. The fundamental theorems about such ideals are due to Zariski found in appendix 5 of [26]. These results were proved by Zariski in [27] for 2dimensional polynomial rings over an algebraically closed field of characteristic zero and rings of holomorphic functions. Zarisk...