Rings and groups with commuting powers

International Journal of Mathematics and Mathematical Sciences

卷:4

Adil Yaqub¹  Hazar Abu-Khuzam¹ 

[1] DEPARTMENT OF MATHEMATICS, PETROLEUM UNIVERSITY, Saudi Arabia;

关键词: ring;    group;    center;    Jacobson radical;    commutative.;   

DOI  :  10.1155/S0161171281000069

来源: DOAJ

【 摘 要 】

Let n be a fixed positive integer. Let R be a ring with identity which satisfies (i) xnyn=ynxn for all x,y in R, and (ii) for x,y in R, there exists a positive integer k=k(x,y) depending on x and y such that xkyk=ykxkand (n,k)=1. Then R is commutative. This result also holds for a group G. It is further shown that R and G need not be commutative if any of the above conditions is dropped.

【 授权许可】

Unknown