The Artin conjecture for Q-algebras.
We give a simplification, in the case of Q-algebras, of the proof of Artin's Conjecture, which says that a regular morphism between Noetherian rings is the inductive limit of smooth morphisms of finite type.
The containment property for large quotient rings.
The differential spectrum of a ring
The Divisor Class Group of Ordinary and Symbolic Blow-ups.
The divisor of the resultant.
The equality in Buchsbaum rings
The factorization of the derivative of Dickson polynomials.
The group of automorphisms of a commutative algebra.
The identity of three classes of polynomials.
The injectivity of Frobenius acting on cohomology and local cohomology modules.
The intersection of distinct Galois subrings is not necessarily Galois
The inverse function theorem for free associative algebras.
The local lifting problem for actions of finite groups on curves
Let be an algebraically closed field of characteristic . We study obstructions to lifting to characteristic the faithful continuous action of a finite group on . To each such a theorem of Katz and Gabber associates an action of on a smooth projective curve over . We say that the KGB obstruction of vanishes if acts on a smooth projective curve in characteristic in such a way that and have the same genus for all subgroups . We determine for which the KGB obstruction...
The number of zeros of polynomials in valuation rings of complete discretely valued fields
The order of algebras with nontrivial fixed point subalgebras.
The Primary components of and Integral Closures of Ideals in 3-Dimensional Regular Local Rings.
The quasi-real extension of the real numbers
The reflectiveness of covering morphisms in algebra and geometry.
The Rings Which Can Be Recovered by Means of the Difference
It is well known that to every Boolean ring can be assigned a Boolean algebra whose operations are term operations of . Then a symmetric difference of together with the meet operation recover the original ring operations of . The aim of this paper is to show for what a ring a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular, we reached...
The -transform and its dual with applications to Prüfer extensions