Wyniki wyszukiwania

1

A counterexample to a conjecture of Bass, Connell and Wright

100%

Ossowski P.

Colloquium Mathematicum

|

1998

|

tom 77

|

nr 2

315-320

EN

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=(G_1,...,G_n) 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 $G_i^{(d)}=\sum_T α(T)^{-1} σ_i(T)$, where T varies over rooted trees with d vertices, α(T)=CardAut(T) and $σ_i(T)$ is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, $F$ is an automorphism or, equivalently, $G_i^{(d)}$ is zero for sufficiently large d. Bass, Connell and Wright conjecture that not only $G_i^{(d)}$ but also the polynomials $σ_i(T)$ are zero for large d. The aim of the paper is to show that for the polynomial automorphism (4) and rooted trees (3), the polynomial $σ_2(T_s)$ is non-zero for any index $s$ (Proposition 4), yielding a counterexample to the above conjecture (see Theorem 5).

2

On the formal inverse of polynomial endomorphisms

100%

Ossowski P.

Colloquium Mathematicum

|

1998

|

tom 78

|

nr 1

97-104

3

Polynomial algebra of constants of the four variable Lotka-Volterra system

63%

Ossowski P., Zieliński J.

Colloquium Mathematicum

|

2010

|

tom 120

|

nr 2

299-309

EN

We describe the ring of constants of a specific four variable Lotka-Volterra derivation. We investigate the existence of polynomial constants in the other cases of Lotka-Volterra derivations, also in n variables.

4

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Derived functors of $\varprojlim$ and abelian ab3- and Ab4-categories with enough injectives

50%

Ossowski P.

Colloquium Mathematicum

|

1981

|

tom 44

|

nr 1

29-33

Ograniczanie wyników

4 Colloquium Mathematicum

4 Ossowski P.

1 Zieliński J.

1 2010

2 1998

1 1981

A counterexample to a conjecture of Bass, Connell and Wright

On the formal inverse of polynomial endomorphisms

Polynomial algebra of constants of the four variable Lotka-Volterra system

Derived functors of $\varprojlim$ and abelian ab3- and Ab4-categories with enough injectives

Ograniczanie wyników

4 Colloquium Mathematicum

4 Ossowski P.

1 Zieliński J.

1 2010

2 1998

1 1981

Wyniki wyszukiwania

A counterexample to a conjecture of Bass, Connell and Wright

On the formal inverse of polynomial endomorphisms

Polynomial algebra of constants of the four variable Lotka-Volterra system

Derived functors of $\varprojlim$ and abelian ab3*- and Ab4*-categories with enough injectives

Derived functors of $\varprojlim$ and abelian ab3- and Ab4-categories with enough injectives