Commutativity theorems for rings and groups with constraints on commutators
Let n>1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn,y]=[x,ym]ys for all x, y in R. If, further, R is n-torsion free, then R is commutativite. If n-torsion freeness of R is replaced by m, n are relatively prime, then R is still commutative. More...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000569 |
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| _version_ | 1832555033091112960 |
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| author | Evagelos Psomopoulos |
| author_facet | Evagelos Psomopoulos |
| author_sort | Evagelos Psomopoulos |
| collection | DOAJ |
| description | Let n>1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn,y]=[x,ym]ys for all x, y in R. If, further, R is n-torsion free, then R is commutativite. If n-torsion freeness of R is replaced by m, n are relatively prime, then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t=s=0 and m=n+1. |
| format | Article |
| id | doaj-art-29eab8092ef444028b5be7314c9bdbaa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-29eab8092ef444028b5be7314c9bdbaa2025-02-03T05:49:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017351351710.1155/S0161171284000569Commutativity theorems for rings and groups with constraints on commutatorsEvagelos Psomopoulos0Department of Mathematics, University of Thessaloniki, Thessaloniki, GreeceLet n>1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn,y]=[x,ym]ys for all x, y in R. If, further, R is n-torsion free, then R is commutativite. If n-torsion freeness of R is replaced by m, n are relatively prime, then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t=s=0 and m=n+1.http://dx.doi.org/10.1155/S0161171284000569commutative ringstorsion free rings. |
| spellingShingle | Evagelos Psomopoulos Commutativity theorems for rings and groups with constraints on commutators International Journal of Mathematics and Mathematical Sciences commutative rings torsion free rings. |
| title | Commutativity theorems for rings and groups with constraints on commutators |
| title_full | Commutativity theorems for rings and groups with constraints on commutators |
| title_fullStr | Commutativity theorems for rings and groups with constraints on commutators |
| title_full_unstemmed | Commutativity theorems for rings and groups with constraints on commutators |
| title_short | Commutativity theorems for rings and groups with constraints on commutators |
| title_sort | commutativity theorems for rings and groups with constraints on commutators |
| topic | commutative rings torsion free rings. |
| url | http://dx.doi.org/10.1155/S0161171284000569 |
| work_keys_str_mv | AT evagelospsomopoulos commutativitytheoremsforringsandgroupswithconstraintsoncommutators |