| A note on the commutativity of semiprime rings |
| Received:December 19, 1983 |
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| Abstract: |
| Awtar proved that a semiprime ring R in which xy2x-yx2y∈Z(center of R)for every x and y in R is commutative. Guo Yuanchun proved that a semiprime ring satisfying (xy)2-xy2x∈Z for every x and y in R is commutative. In this note the following result is proved:A semiprime ring is commutative if R satisfies one of the following conditions:(1) x2y2 -xy2x∈Z for every x and y in R.(2) x2y2-yx2y-y∈Z for every x and y in R.(3) (yx)2 -xy2x∈Z for every x and y in R. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1985.04.026 |
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