Regular ideals in commutative rings, sublattices of regular ideals, and Prüfer rings

Normal Ideals in Regular Rings

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.

Generalizations of Primary Ideals in Commutative Rings

Let R be a commutative ring with identity. Let φ : I(R) → I(R) ∪ {∅} be a function where I(R) denotes the set of all ideals of R. A proper ideal Q of R is called φ-primary if whenever a, b ∈ R, ab ∈ Q−φ(Q) implies that either a ∈ Q or b ∈ √ Q. So if we take φ∅(Q) = ∅ (resp., φ0(Q) = 0), a φ-primary ideal is primary (resp., weakly primary). In this paper we study the properties of several genera...

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...

T -rough Semiprime Ideals on Commutative Rings

Rough sets were originally proposed in the presence of an equivalence relation. An equivalence relation is sometimes difficult to be obtained in rearward problems due to the vagueness and incompleteness of human knowledge. The purpose of this paper is to introduce and discuss the concept of T -rough semiprime ideal, T -rough fuzzy semiprime ideal and T -rough quotient ideal in a commutative rin...