This article concerns commutative factor rings for ideals contained in the center. A ring $R$ is called CIFC if $R/I$ some proper ideal $I$ of with $I\subseteq Z(R)$, where $Z(R)$ center $R$. We prove that (i) a $R$, $W(R)$ contains all nilpotent elements (hence Köthe's conjecture holds $R$) and $R/W(R)$ reduced ring; (ii) strongly bounded $R/N_*(R)$ $0\neq N_*(R)\subseteq (resp., $N_*(R)$) Wed...

Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I . It is shown that the minimal generators of Rs(I) are in one to one correspondence with the irreducible parallelizations of C. From our description some major results on symbolic Rees algebras of perfect graphs and clutters will follow. As a b...

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 $R$,...

Call a compact Riemannian manifold M a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from M contains elements of arbitrarily small energy. If M is isometrically immersed in Euclidean space, then a condition on the second fundamental form of M is given which implies M is strongly unstable. As compact ...

It is shown that the discriminant of a discriminant has the same irreducible factors as the product of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under tame conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideal, while the four other are equal to one. Moreover the factors of two of thes...

It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the diameter and the average distance of the graph on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural to...