A Cancellation Theorem for Projective Modules in the Metastable Range.
A class of counterexamples to the Cancellation Problem for arbitrary rings
We present a class of counterexamples to the Cancellation Problem over arbitrary commutative rings, using non-free stably free modules and locally nilpotent derivations.
A class of torsion-free abelian groups characterized by the ranks of their socles
Butler groups formed by factoring a completely decomposable group by a rank one group have been studied extensively. We call such groups, bracket groups. We study bracket modules over integral domains. In particular, we are interested in when any bracket -module is tensor a bracket group.
A Condition for a Polynomial Map to be Invertible.
A counterexample to a conjecture of Bass, Connell and Wright
Let F=X-H: → be a polynomial map with H homogeneous of degree 3 and nilpotent Jacobian matrix J(H). Let G=(G1,...,Gn) be the formal inverse of F. Bass, Connell and Wright proved in [1] that the homogeneous component of of degree 2d+1 can be expressed as , where T varies over rooted trees with d vertices, α(T)=CardAut(T) and is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, is an automorphism or, equivalently, is zero for sufficiently large d....
A homological characterization of local complete intersections
A monogenic Hasse-Arf theorem
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
A Norm for Modules and Algebras.
A Note on Derivations of Commutative Rings.
A note on finitely generated commutative rings
A note on Nakai’s conjecture for the ring
A note on perfect modules over crossed products
A note on the computation of multiplicities.
A note on the one-dimensional systems of formal equations
On this paper we compute the numerical function of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
A numerical criterion for the permissibility of a blowing-up
A primrose path from Krull to Zorn
Given a set of “indeterminates” and a field , an ideal in the polynomial ring is called conservative if it contains with any polynomial all of its monomials. The map yields an isomorphism between the power set and the complete lattice of all conservative prime ideals of . Moreover, the members of any system of finite character are in one-to-one correspondence with the conservative prime ideals contained in , and the maximal members of correspond to the maximal ideals contained in...
A property of non excellent rings.
À propos des théories de Galois finies et infinies
A remark on the quadratic analogue of the Quillen-Suslin theorem.
A short proof of a fibre criterion for polynomials to belong to an ideal.