On Nil-Symmetric Rings
The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring R is called right (left) nil-symmetric if, for a,b,c∈R, where a,b are nilpotent elements, abc=0 (cab=0) implies acb=0. A ring is called nil-symmet...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/483784 |
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| Summary: | The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring R is called right (left) nil-symmetric if, for a,b,c∈R, where a,b are nilpotent elements, abc=0 (cab=0) implies acb=0. A ring is called nil-symmetric if it is both right and left nil-symmetric. It has been shown that the polynomial ring over a nil-symmetric ring may not be a right or a left nil-symmetric ring. Further, it is also proved that if R is right (left) nil-symmetric, then the polynomial ring R[x] is a nil-Armendariz ring. |
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| ISSN: | 2314-4629 2314-4785 |