Rings and groups with commuting powers

Hazar Abu-Khuzam and Adil Yaqub

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-7

Abstract:

Let n be a fixed positive integer. Let R be a ring with identity which satisfies (i) x n y n = y n x n 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 x k y k = y k x k and ( 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.

Date: 1981
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/4/427649.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/4/427649.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:427649

DOI: 10.1155/S0161171281000069

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().