On the global dimension of some filtered algebras

This article does not have an abstract

A note on geometric factoriality

This article does not have an abstract

Generalized epimorphism theorem

Let R[X, Y] be a polynomial ring in two variables over a commutative ringR and let F∈ R[X, Y] such that R[X, Y]/(F)=R[Z] (a polynomial ring in one variable). In this set-up we prove that R[X, Y]= R[F, G] for some G ∈R[X, Y] if either R contains a field of characteristic zero or R is a seminormal domain of characteristic zero

A Question of Nori: Projective Generation of Ideals

Abstract. Let A be a smooth affine domain of dimension d over an infinite perfect field k and let n be an integer such that 2n . Under these assumptions, it is proved in this paper that I Mathematics Subject Classification

Zero-divisor graphs of nilpotent-free semigroups

We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs.Comment: Expanded first paragraph in section 6. To appear in J. Algebraic Combin. 22 page

A note on projective modules over polynomial rings

This article does not have an abstract

On the global dimension of some filtered algebras (II)

This article does not have an abstract

On the centre of some filtered algebras

This article does not have an abstract