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| 蕴涵环交换性的某些多项恒等式 | |
| 作者姓名： | Ashraf M Jacob V W |
| 作者单位： | Department of Mathematics，Aligarh Muslim University，Aligarh，202002，India |
| 摘 要： | 设ｍ＞１，ｎ，ｐ，ｑ，ｒ，ｓ均为正整数，Ｒ是一个具有单位元１的环．证明了：如果Ｒ中的任意ｘ，ｙ满足且Ｒ具有Ｑ（ｍ）性质，则Ｒ是一个交换环．此外，在适当的条件下确立了Ｒ的交换性． |
| 关 键 词： | 多项恒等式，交换性，扭自由环，换位子理想 |
On Certain Polynomial Identities Implying Commutativity for Rings |
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| Ashraf M,Jacob V W.On Certain Polynomial Identities Implying Commutativity for Rings[J].Journal of Jilin University: Sci Ed,1996(2). | |
| Authors: | Ashraf M Jacob V W |
| Abstract: | Let m>1,n,p,q,r,s be fixed non-negative integers and R be a ring with unity 1satisfying either of the polynomial identitiesfor all x,y in R.The main result of the present paper asserts that R is commutative if R possesses Q(m)property(that is for all x,y in R,mx,y]=0 impliesx,y]=0).Also,under different appropriate constraints on the integral exponents,the commutativity of R has been established. |
| Keywords: | polynomial identities commutators torsion free rings commutator ideal |
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