Maps Preserving Idempotence on Matrix Spaces
Suppose F is an arbitrary field. Let |F| be the number of the elements of F. Let Mn(F) be the space of all n×n matrices over F, let Sn(F) be the subset of Mn(F) consisting of all symmetric matrices, and let Tn(F) be the subset of Mn(F) consisting of all upper-triangular matrices. Let V∈{Sn(F),Mn(F),...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/428203 |
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| Summary: | Suppose F is an arbitrary field. Let |F| be the number of the elements of F. Let Mn(F) be the space of all n×n matrices over F, let Sn(F) be the subset of Mn(F) consisting of all symmetric matrices, and let Tn(F) be the subset of Mn(F) consisting of all upper-triangular matrices. Let V∈{Sn(F),Mn(F),Tn(F)}; a map Φ:V→V is said to preserve idempotence if A-λB is idempotent if and only if Φ(A)-λΦ(B) is idempotent for any A,B∈V and λ∈F. In this paper, the maps preserving idempotence on Sn(F), Mn(F), and Tn(F) were characterized in case |F|=3. |
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| ISSN: | 2314-4629 2314-4785 |