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.
A Note About the Nowicki Conjecture on Weitzenböck Derivations
2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant theory.
A Note On A Class Of Noetherian Rings
A note on a class of Noetherian rings.
A Note on a Paper by Miyazaki.
A note on Abhyankar-Moh's approximate roots of polynomials.
A note on approximation theorems
A note on basic free modules and the condition.
A note on Bézout's theorem
We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.
A note on characterizations of rings of constants with respect to derivations
Let A be a commutative algebra without zero divisors over a field k. If A is finitely generated over k, then there exist well known characterizations of all k-subalgebras of A which are rings of constants with respect to k-derivations of A. We show that these characterizations are not valid in the case when the algebra A is not finitely generated over k.
A Note on Derivations of Commutative Rings.
A Note on Elementary Derivations
2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.Let R be a UFD containing a field of characteristic 0, and Bm = R[Y1, . . . , Ym] be a polynomial ring over R. It was conjectured in [5] that if D is an R-elementary monomial derivation of B3 such that ker D is a finitely generated R-algebra then the generators of ker D can be chosen to be linear in the Yi ’s. In this paper, we prove that this does not hold for B4. We also investigate R-elementary derivations D of Bm...
A note on extensions of algebraic and formal gorups I.