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 $R$,...

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...

We give an explicit construction, for a flat map X → S of algebraic spaces, of an ideal in the n’th symmetric product of X over S. Blowing up this ideal is then shown to be isomorphic to the schematic closure in the Hilbert scheme of length n subschemes of the locus of n distinct points. This generalises Haiman’s corresponding result ([13]) for the affine complex plane. However, our constructio...

It is well known that the set of all ideals(2) of a ring forms a complete modular lattice with respect to set inclusion. The same is true of the set of all right ideals. Our purpose in this paper is to consider the consequences of imposing certain additional restrictions on these ideal lattices. In particular, we discuss the case in which one or both of these lattices is complemented, and the c...

Let $$L_n$$ be a line graph with n edges and $${{\mathcal {F}}}(L_n)$$ the facet ideal of its matching complex. In this paper, we provide irreducible decomposition some exact formulas for projective dimension regularity .

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. We are concerned with the following question: Which algebras are homomorphic images of subdirectly irreducible algebras? A necessary condition, discovered...