We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some con...

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.

Let R be a non-domain commutative ring with identity and A(R) be theset of non-zero ideals with non-zero annihilators. We call an ideal I of R, anannihilating-ideal if there exists a non-zero ideal J of R such that IJ = (0).The annihilating-ideal graph of R is defined as the graph AG(R) with the vertexset A(R) and two distinct vertices I and J are adjacent if and only if IJ =(0). In this paper,...

Let R be a commutative ring with identity. An ideal I in R is called a multiplication ideal if every ideal contained in I is a multiple of I. Ohm's properties for nitely generated ideals in Pr ufer domains are investigated by Gilmer. These properties are generalized by Naoum and studied for nitely generated multiplication ideals. The purpose of this work is to generalize the results of Gilmer a...

We prove that each ideal of a locally formally equidimensional analytically un-ramiied Noetherian integral domain is the contraction of an ideal of a one-dimensional semilo-cal birational extension domain. We give an application to a problem concerning the primary decomposition of powers of ideals in Noetherian rings. It is shown in S2] that for each ideal I in a Noetherian commutative ring R t...

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discrete uniformization via hyper-ideal circle patterns always exists and is uniqu...

Throughout our discussion, all rings are commutative, Noetherian and have an identity element. The notion of the tight closure of an ideal was developed by M. Hochster and C. Huneke in [HH1] and has yielded many elegant and powerful results in commutative algebra. The theory leads to the notion of F–rational rings, defined by R. Fedder and K.-i. Watanabe as rings in which parameter ideals are t...

Definition 2.1. A commutative ring R is Noetherian if every chain of ideals in R I0 ⊂ I1 ⊂ I2 ⊂ · · · terminates after a finite number of steps (i.e., there is an interger k such that Is = Ik if s ≥ k). Remark 2.2. Polynomial rings R [X1, . . . , Xn] are Noetherian if R is. In particular, S (p) = C [p∗] is Noetherian. Theorem 2.3. If R is a Noetherian ring, and M is a finitely generated R-modul...

Let R denote a commutative local ring with maximal ideal m and residue field k — R/m. In this paper we determine the group automorphisms of the general linear group GL (R) when n > 3 and the characteristic of k is not 2.