On Prime Ideals in Representation Rings.
On Prüfer v-Multiplication Domains.
On ring derivations and quadratic functionals.
On Separable Subalgebras of Azumaya Algebras
On some properties of pure morphisms of commutative rings.
On Splitting Rings for Azumaya Skew Group Rings
On Strong Going-Between, Going-Down, And Their Universalizations, II
We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if are domains such that is an LFD universally going-down domain and is algebraic over , then the inclusion map satisfies GB for each . However, for any nonzero ring...
On strongly affine extensions of commutative rings
A ring extension is said to be strongly affine if each -subalgebra of is a finite-type -algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if is a quasi-local ring of finite dimension, then is integrally closed and strongly affine if and only if is a Prüfer extension (i.e. is a normal pair). As a consequence, the equivalence of strongly affine extensions, quasi-Prüfer extensions and INC-pairs is shown. Let be...
On the Anderson-Badawi conjecture
Let be a commutative ring with an identity different from zero and be a positive integer. Anderson and Badawi, in their paper on -absorbing ideals, define a proper ideal of a commutative ring to be an -absorbing ideal of , if whenever for , then there are of the ’s whose product is in and conjecture that for any ideal of an arbitrary ring , where . In the present paper, we use content formula techniques to prove that their conjecture is true, if one of the following conditions...
On the Bass-Quillen Conjecture Concerning Projective Modules Over Polynomial Rings.
On the Complete Integral Closure of a Mori Domain
On the construction of explicit solutions to the matrix equation .
On the equivalence of algebraic and geometric local cohomology
In this paper, we will present several necessary and sufficient conditions on a commutative ring such that the algebraic and geometric local cohomologies are equivalent.
On the Finite Generation of Symbolic Blow-Ups.
On the formal inverse of polynomial endomorphisms
On the Galois structure of the square root of the codifferent
Let be a finite abelian extension of , with the ring of algebraic integers of . We investigate the Galois structure of the unique fractional -ideal which (if it exists) is unimodular with respect to the trace form of .
On the generalization of the Fibonacci-coefficient polynomials.
On the geometrization of a lemma of Singer and van der Put
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory, used by Singer and van der Put in their reference book. This geometrization, in addition of giving a nice insight on this result, offers us the opportunity to investigate several points of differential algebra and differential algebraic geometry. We study the class of simple Δ-schemes and prove that they all have a coarse space of leaves. Furthermore, instead of considering schemes endowed with...
On the integral closure of ideals.
On the irreducibility of pure difference binomials.