the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

The main result of this paper is the explicit determination of the core of integrally closed ideals in two-dimensional regular local rings. The core of an ideal I in a ring R was introduced by Judith Sally in the late 1980's and alluded to in Rees and Sally's paper RS]. Recall that a reduction of I is any ideal J for which there exists an integer n such that JI n = I n+1 NR]. In other words, J ...

Let k be an algebraically closed field. We will employ the following notation. If I ⊂ k[X1, . . . , Xn] is an ideal, we let Z(I) denote the affine algebraic set in An defined by the vanishing of the polynomials in I . Conversely, if X is an affine algebraic set, I(X) denotes the ideal of polynomials in k[X1, . . . , Xn] vanishing on X . We will give a proof of the following result, called the w...

Let E be a central extension of the form 0 → V → G → W → 0 where V and W are elementary abelian 2-groups. Associated to E there is a quadratic map Q : W → V given by the 2-power map which uniquely determines the extension. This quadratic map also determines the extension class q of the extension in H(W,V ) and an ideal I(q) in H(G,Z/2) which is generated by the components of q. We say E is Bock...

A fuzzy ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under arbitrary union and finite intersections. In this paper, we introduce a weak form of fuzzy ideals namely fuzzy pre-ideals and a way to obtain new fuzzy topologies is presented in this paper. Furthermore some interesting results for fuzzy ideals are generalized to fuzzy pre-ideal.

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [25], Kostyrko et. al introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number `, if for each ε > 0 the set {k ∈ N : |xk − `| ≥ ε} belongs to I. In this article we introduce the concept of ideal conv...

We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms. Finally, we give an upper bound for the Castelnuovo-Mumford regularity of the binomial edge ideal of...

Theorem. A commutative B*-algebra K containing an identity e (with \\k*-k\\ =\\k\\2for all &GP and ||e|| =1) is isomorphic (in a norm and * preserving manner) to an algebra B(X) of all bounded complexvalued functions on an essentially unique set X if and only if: (1) Every nonzero closed ideal of K contains a minimal ideal; (2) The sum of two annulets is an annulet. An annulet is here understoo...