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A Cancellation Theorem for Projective Modules in the Metastable Range.

Inventiones mathematicae

A class of counterexamples to the Cancellation Problem for arbitrary rings

Annales Polonici Mathematici

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.

Mathematische Annalen

A counterexample to a conjecture of Bass, Connell and Wright

Colloquium Mathematicae

Let F=X-H:${k}^{n}$${k}^{n}$ 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  that the homogeneous component of ${G}_{i}$ of degree 2d+1 can be expressed as ${G}_{i}^{\left(d\right)}={\sum }_{T}\alpha {\left(T\right)}^{-1}{\sigma }_{i}\left(T\right)$, where T varies over rooted trees with d vertices, α(T)=CardAut(T) and ${\sigma }_{i}\left(T\right)$ is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, $F$ is an automorphism or, equivalently, ${G}_{i}^{\left(d\right)}$ is zero for sufficiently large d....

A primrose path from Krull to Zorn

Commentationes Mathematicae Universitatis Carolinae

Given a set $X$ of “indeterminates” and a field $F$, an ideal in the polynomial ring $R=F\left[X\right]$ is called conservative if it contains with any polynomial all of its monomials. The map $S↦RS$ yields an isomorphism between the power set $\text{P}\phantom{\rule{0.166667em}{0ex}}\left(X\right)$ and the complete lattice of all conservative prime ideals of $R$. Moreover, the members of any system $\text{S}\phantom{\rule{0.166667em}{0ex}}\subseteq \text{P}\phantom{\rule{0.166667em}{0ex}}\left(X\right)$ of finite character are in one-to-one correspondence with the conservative prime ideals contained in ${P}_{\text{S}}=\bigcup \left\{RS:S\in \text{S}\phantom{\rule{0.166667em}{0ex}}\right\}$, and the maximal members of $\text{S}\phantom{\rule{0.166667em}{0ex}}$ correspond to the maximal ideals contained in...

A remark on the quadratic analogue of the Quillen-Suslin theorem.

Journal für die reine und angewandte Mathematik

A short proof of a fibre criterion for polynomials to belong to an ideal.

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Abelsche Galoiserweiterungen von R[X].

Manuscripta mathematica

Abhyankar-Moh property and unique affine embeddings.

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Addendum to Polynomial rings over Jacobson-Hilbert rings.

Publicacions Matemàtiques

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.

Journal für die reine und angewandte Mathematik

An Effective Approach to Keller's Jacobian Conjecture.

Mathematische Annalen

Anisotropic resultant. Complements and applications. (Résultant anisotrope. Compléments et applications.)

The Electronic Journal of Combinatorics [electronic only]

Applications polynômiales à jacobienne constante

Seminaire de Théorie des Nombres de Bordeaux

Associate forms, joins, multiplicities and an intrinsic elimination theory

Banach Center Publications

Autour des idéaux premiers de Goldman d'un anneau commutatif

Annales scientifiques de l'Université de Clermont. Mathématiques

Acta Arithmetica

Bounds in the theory of polynomial rings over fields. A nonstandard approach.

Inventiones mathematicae

Commutative Rings and Binomial Coefficients.

Monatshefte für Mathematik

Acta Arithmetica

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