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 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 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 remark on the quadratic analogue of the Quillen-Suslin theorem.
A short proof of a fibre criterion for polynomials to belong to an ideal.
Abelsche Galoiserweiterungen von R[X].
Abhyankar-Moh property and unique affine embeddings.
Addendum to Polynomial rings over Jacobson-Hilbert rings.
In the article appeared in this same journal, vol. 33, 1 (1989) pp. 85-97, some statements in the proof of Example 3.4B got scrambled.
Algebraic closure of modules.
An Effective Approach to Keller's Jacobian Conjecture.
Anisotropic resultant. Complements and applications. (Résultant anisotrope. Compléments et applications.)
Applications polynômiales à jacobienne constante
Associate forms, joins, multiplicities and an intrinsic elimination theory
Autour des idéaux premiers de Goldman d'un anneau commutatif
Bounds for the degrees in the membership test for a polynomial ideal
Bounds in the theory of polynomial rings over fields. A nonstandard approach.
Characterization of irreducible polynomials over a special principal ideal ring
A commutative ring with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length . Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length .
Commutative Rings and Binomial Coefficients.