A Geometrie Approach to Keller's Jacobian Conjecture.
A graph associated to proper non-small ideals of a commutative ring
In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring , denoted by , is a graph with all non-small proper ideals of as vertices and two distinct vertices and are adjacent if and only if is not small in . In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter,...
A homological characterization of local complete intersections
A homological proof of a theorem by Davis, Geramita, Orecchia giving the Cayley-Bacharach theorem.
A hypervaluation of a ring onto a totally ordered non-cancellative semigroup without zero divisors.
A K-Theoretic Approach to Multiplicities.
A local characterization of Prüfer rings.
A lower bound for coherences on the Brown-Peterson spectrum.
A measure theoretic approach to logical quantification
A method to estimate the degree of -sufficiency of analytic functions.
A minimal Set of Generators for the Ring of multisymmetric Functions
The purpose of this article is to give, for any (commutative) ring , an explicit minimal set of generators for the ring of multisymmetric functions as an -algebra. In characteristic zero, i.e. when is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...
A model-theoretic transfer theorem for henselian valued fields.
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A natural map from the ext Künneth sequence to the Tor one.
A new algebraic criterion for shellability.
A new algorithm for the Quillen-Suslin theorem.
A new characterization of rational surface singularities.
A new version of Local-Global Principle for annihilations of local cohomology modules
Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of relative to in the context of generalized local cohomology modules as , where M is an R-module. We also show that for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.
A nonlinearizable action of on
The main purpose of this article is to give an explicit algebraic action of the group of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.
A Norm for Modules and Algebras.