微分多项式环的半交换性和对称性

The semicommutativity and symmetry of differential polynomial rings

研究微分多项式环R[x;δ]和Ore扩张环R[x;α,δ]的广义半交换性质和广义对称性质,使用逐项分析方法证明了:设R是δ-Armendariz环,则R[x;δ]是诣零半交换环(弱半交换环、广义弱对称环、弱zip环、右弱McCoy环)当且仅当R是诣零半交换环(弱半交换环、广义弱对称环、弱zip环、右弱McCoy环);设R是弱2-素环和(α,δ)-条件环,则R[x;α,δ]是诣零半交换环(分别地,弱半交换环,广义弱对称环).

This paper investigates the generalized semicommutativity and generalized symmetry of the differential pol‐ynomial rings and Ore extensions of a ring .By using the itemized analysis method on polynomials ,we proved that if R is δ‐Armendariz ring ,then R[x;δ] is nil‐semicommutative ring （resp .,weakly semicommutative ,generalized weak symmetry （GWS） ,weak zip ,right weak McCoy） if and only if R is nil‐semicommutative ring （resp .,weakly semicommutative ,GWS ,weak zip ,right weak McCoy） .Moreover ,if R is a weakly 2‐primal and （α,δ）‐condition ring ,then R[x;α,δ] is nil‐semicommutative ring （resp .,weakly semicommutative ,GWS） .