On the mapping xy→(xy)n in an associative ring
We consider the following condition (*) on an associative ring R:(*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy)=(xy)n(x,y) for some positive integer n(x,y)>1. Commutativity and structure are established for Artinian rin...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204208250 |
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| author | Scott J. Beslin Awad Iskander |
| author_facet | Scott J. Beslin Awad Iskander |
| author_sort | Scott J. Beslin |
| collection | DOAJ |
| description | We consider the following condition (*) on an associative ring
R:(*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is
injective on R2, and f(xy)=(xy)n(x,y) for some
positive integer n(x,y)>1. Commutativity and structure are
established for Artinian rings R satisfying (*), and a
counterexample is given for non-Artinian rings. The results
generalize commutativity theorems found elsewhere. The case n(x,y)=2 is examined in detail. |
| format | Article |
| id | doaj-art-0a7870d8954941129b3a770be12a944b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0a7870d8954941129b3a770be12a944b2025-02-03T01:01:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004261393139610.1155/S0161171204208250On the mapping xy→(xy)n in an associative ringScott J. Beslin0Awad Iskander1Department of Mathematics and Computer Science, Nicholls State University, Thibodaux 70310, LA, USADepartment of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USAWe consider the following condition (*) on an associative ring R:(*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy)=(xy)n(x,y) for some positive integer n(x,y)>1. Commutativity and structure are established for Artinian rings R satisfying (*), and a counterexample is given for non-Artinian rings. The results generalize commutativity theorems found elsewhere. The case n(x,y)=2 is examined in detail.http://dx.doi.org/10.1155/S0161171204208250 |
| spellingShingle | Scott J. Beslin Awad Iskander On the mapping xy→(xy)n in an associative ring International Journal of Mathematics and Mathematical Sciences |
| title | On the mapping xy→(xy)n in an
associative ring |
| title_full | On the mapping xy→(xy)n in an
associative ring |
| title_fullStr | On the mapping xy→(xy)n in an
associative ring |
| title_full_unstemmed | On the mapping xy→(xy)n in an
associative ring |
| title_short | On the mapping xy→(xy)n in an
associative ring |
| title_sort | on the mapping xy xy n in an associative ring |
| url | http://dx.doi.org/10.1155/S0161171204208250 |
| work_keys_str_mv | AT scottjbeslin onthemappingxyxyninanassociativering AT awadiskander onthemappingxyxyninanassociativering |