Reversible Rings with Involutions and Some Minimalities
In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, *-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and exam...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/650702 |
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| author | W. M. Fakieh S. K. Nauman |
| author_facet | W. M. Fakieh S. K. Nauman |
| author_sort | W. M. Fakieh |
| collection | DOAJ |
| description | In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, *-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of *-reversible rings. It is proved here that the polynomial rings of *-reversible rings may not be *-reversible. A criterion for rings which cannot adhere to any involution is developed and it is observed that a minimal noninvolutary ring is of order 4 and that a minimal noncommutative *-reversible ring is of order 16. |
| format | Article |
| id | doaj-art-af70a2a4da68464282c78975ede8fcdd |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-af70a2a4da68464282c78975ede8fcdd2025-02-03T06:05:00ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/650702650702Reversible Rings with Involutions and Some MinimalitiesW. M. Fakieh0S. K. Nauman1Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaFaculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaIn continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, *-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of *-reversible rings. It is proved here that the polynomial rings of *-reversible rings may not be *-reversible. A criterion for rings which cannot adhere to any involution is developed and it is observed that a minimal noninvolutary ring is of order 4 and that a minimal noncommutative *-reversible ring is of order 16.http://dx.doi.org/10.1155/2013/650702 |
| spellingShingle | W. M. Fakieh S. K. Nauman Reversible Rings with Involutions and Some Minimalities The Scientific World Journal |
| title | Reversible Rings with Involutions and Some Minimalities |
| title_full | Reversible Rings with Involutions and Some Minimalities |
| title_fullStr | Reversible Rings with Involutions and Some Minimalities |
| title_full_unstemmed | Reversible Rings with Involutions and Some Minimalities |
| title_short | Reversible Rings with Involutions and Some Minimalities |
| title_sort | reversible rings with involutions and some minimalities |
| url | http://dx.doi.org/10.1155/2013/650702 |
| work_keys_str_mv | AT wmfakieh reversibleringswithinvolutionsandsomeminimalities AT sknauman reversibleringswithinvolutionsandsomeminimalities |