广义线性McCoy环(英文)

Generalized Linearly McCoy Rings

称环R是右线性McCoy的,如果R[x]中非零线性多项式f(x),g(x)满足f(x)g(x)=0,则存在非零元素r∈R使得f(x)r=0.设α是环R的自同态,通过用斜多项式环R[x;α]中的元素代替一般多项式环R[x]中的元素而引入α-线性McCoy环的概念.讨论了α-线性McCoy环的基本性质和扩张性质.

A ring R is called right linearly McCoy, if whenever linear polynomials f（x）, g（x） E R[x]／{0} satisfy f（x）g（x） = 0, there exists r E R／{0} such that f（x）r = 0. For a ring endomorphism a, we introduce the notion of an a-linearly McCoy ring by considering the polynomials in the skew polynomial ring R[x; a] in place of the ring R[x]. A number of properties of this generalization are established and extension properties of a-linearly McCoy rings are given.