Rings and groups with commuting powers
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 fur...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000069 |
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| _version_ | 1832564529356079104 |
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| author | Hazar Abu-Khuzam Adil Yaqub |
| author_facet | Hazar Abu-Khuzam Adil Yaqub |
| author_sort | Hazar Abu-Khuzam |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-423d95122b22484a98c73ef9545cea2b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-423d95122b22484a98c73ef9545cea2b2025-02-03T01:10:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014110110710.1155/S0161171281000069Rings and groups with commuting powersHazar Abu-Khuzam0Adil Yaqub1DEPARTMENT OF MATHEMATICS, PETROLEUM UNIVERSITY, Saudi ArabiaDEPARTMENT OF MATHEMATICS, PETROLEUM UNIVERSITY, Saudi ArabiaLet 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.http://dx.doi.org/10.1155/S0161171281000069ringgroupcenterJacobson radicalcommutative. |
| spellingShingle | Hazar Abu-Khuzam Adil Yaqub Rings and groups with commuting powers International Journal of Mathematics and Mathematical Sciences ring group center Jacobson radical commutative. |
| title | Rings and groups with commuting powers |
| title_full | Rings and groups with commuting powers |
| title_fullStr | Rings and groups with commuting powers |
| title_full_unstemmed | Rings and groups with commuting powers |
| title_short | Rings and groups with commuting powers |
| title_sort | rings and groups with commuting powers |
| topic | ring group center Jacobson radical commutative. |
| url | http://dx.doi.org/10.1155/S0161171281000069 |
| work_keys_str_mv | AT hazarabukhuzam ringsandgroupswithcommutingpowers AT adilyaqub ringsandgroupswithcommutingpowers |