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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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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| author | Yuqiu Sheng Hanyu Zhang |
| author_facet | Yuqiu Sheng Hanyu Zhang |
| author_sort | Yuqiu Sheng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d3b0512262bb406b94d096a71db65341 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d3b0512262bb406b94d096a71db653412025-02-03T06:01:44ZengWileyJournal of Mathematics2314-46292314-47852015-01-01201510.1155/2015/428203428203Maps Preserving Idempotence on Matrix SpacesYuqiu Sheng0Hanyu Zhang1School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaSuppose 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.http://dx.doi.org/10.1155/2015/428203 |
| spellingShingle | Yuqiu Sheng Hanyu Zhang Maps Preserving Idempotence on Matrix Spaces Journal of Mathematics |
| title | Maps Preserving Idempotence on Matrix Spaces |
| title_full | Maps Preserving Idempotence on Matrix Spaces |
| title_fullStr | Maps Preserving Idempotence on Matrix Spaces |
| title_full_unstemmed | Maps Preserving Idempotence on Matrix Spaces |
| title_short | Maps Preserving Idempotence on Matrix Spaces |
| title_sort | maps preserving idempotence on matrix spaces |
| url | http://dx.doi.org/10.1155/2015/428203 |
| work_keys_str_mv | AT yuqiusheng mapspreservingidempotenceonmatrixspaces AT hanyuzhang mapspreservingidempotenceonmatrixspaces |