92 research outputs found
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
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