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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| Format: | Article |
| Language: | English |
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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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| author | Uday Shankar Chakraborty Krishnendu Das |
| author_facet | Uday Shankar Chakraborty Krishnendu Das |
| author_sort | Uday Shankar Chakraborty |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5cb433c95b584ad38f3c4f6b348e054f |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5cb433c95b584ad38f3c4f6b348e054f2025-02-03T01:28:45ZengWileyJournal of Mathematics2314-46292314-47852014-01-01201410.1155/2014/483784483784On Nil-Symmetric RingsUday Shankar Chakraborty0Krishnendu Das1Department of Mathematics, Albert Einstein School of Physical Sciences, Assam University, Silchar, Assam 788011, IndiaDepartment of Mathematics, Netaji Subhas Mahavidyalaya, Udaipur, Tripura 799120, IndiaThe 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.http://dx.doi.org/10.1155/2014/483784 |
| spellingShingle | Uday Shankar Chakraborty Krishnendu Das On Nil-Symmetric Rings Journal of Mathematics |
| title | On Nil-Symmetric Rings |
| title_full | On Nil-Symmetric Rings |
| title_fullStr | On Nil-Symmetric Rings |
| title_full_unstemmed | On Nil-Symmetric Rings |
| title_short | On Nil-Symmetric Rings |
| title_sort | on nil symmetric rings |
| url | http://dx.doi.org/10.1155/2014/483784 |
| work_keys_str_mv | AT udayshankarchakraborty onnilsymmetricrings AT krishnendudas onnilsymmetricrings |