On Form Ideals and Artin-Rees Condition.
On generating sets of minimal length for polynomial ideals
On h-regular graded algebras
On h-regular grades algebras of characteristic p > 0
On induced modules over strongly group-graded algebras.
On modules and rings with the restricted minimum condition
A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.
On modules in which idempotent reducts form a chain
On prime divisors of the integral closure of a principal ideal.
On soluble groups of module automorphisms of finite rank
Let be a commutative ring, an -module and a group of -automorphisms of , usually with some sort of rank restriction on . We study the transfer of hypotheses between and such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose is -Noetherian. If has finite rank, then also is -Noetherian. Further, if is -Noetherian and if only certain abelian sections...
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 Symmetric Algebras which are Cohen Macaulay.
On the algebraic compactness of some complete modules
On the biggest maximaly generated ideal as the conductor in the blowing up ring.
On the canonical element conjecture II.
On the Cantor-Bendixson rank of metabelian groups
We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank .
On the Complete Integral Closure of a Mori Domain
On the ...-Dimension of Cartesian Squares.
On the family relation for artinian rings
On the Finite Generation of Symbolic Blow-Ups.
On the Forster-Eisenbud-Evans Conjectures.