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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 [1] 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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