多项式代数的收缩

On Retracts of Polynomial Algebras

研究特征零的域k上n元多项式代数k[n]收缩R的结构.证明了:1)若Rk[r],其中r<n-1/2,则有k[n]的自同构ψ,使得ψ(R)=k[x1+h1,…,xr+hr],其中每个hi属于理想〈xr+1,…,xn〉;2)若R是某个齐次收缩同态的满同态像,则R同构于一个多项式代数.

We investigated the structure of a retract R of k[n],the polynomial algebra in n variables over a field k of characteristic zero,with the following results proved： 1） if R≌k[r] for some rn-1/2,then there exists an automorphism ψ of k[n],such that ψ（R）=k[x1＋h1,…,xr＋hr],where each hi belongs to 〈xr＋1,…,xn〉;2） if R is the surjective homomorphic image of a homogeneous retraction of k[n],then R is isomorphic to a polynomial algebra.