Rank-one nonincreasing mappings on triangular matrices and some related preserver problems
Let T-n(F) be the algebra of all n x n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings psi: T-n(F) --> T-m(F), n less than or equal to m such that psi (I-n) is of rank n. We next deduce from this result certain types of singular ran...
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| Format: | Article |
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2001
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| Online Access: | http://shdl.mmu.edu.my/2703/ |
| _version_ | 1848790128069181440 |
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| author | Chooi, W. L. Lim, M. H. |
| author_facet | Chooi, W. L. Lim, M. H. |
| author_sort | Chooi, W. L. |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | Let T-n(F) be the algebra of all n x n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings psi: T-n(F) --> T-m(F), n less than or equal to m such that psi (I-n) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on T-n(F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on T-n(F) are also given. |
| first_indexed | 2025-11-14T18:07:41Z |
| format | Article |
| id | mmu-2703 |
| institution | Multimedia University |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:07:41Z |
| publishDate | 2001 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | mmu-27032013-11-11T05:03:04Z http://shdl.mmu.edu.my/2703/ Rank-one nonincreasing mappings on triangular matrices and some related preserver problems Chooi, W. L. Lim, M. H. QA Mathematics Let T-n(F) be the algebra of all n x n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings psi: T-n(F) --> T-m(F), n less than or equal to m such that psi (I-n) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on T-n(F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on T-n(F) are also given. 2001 Article NonPeerReviewed Chooi, W. L. and Lim, M. H. (2001) Rank-one nonincreasing mappings on triangular matrices and some related preserver problems. Linear and Multilinear Algebra, 49 (4). pp. 305-336. ISSN 0308-1087 http://www.tandfonline.com/doi/abs/10.1080/03081080108818703#.UoBkT_ud19o 10.1080/03081080108818703 10.1080/03081080108818703 10.1080/03081080108818703 |
| spellingShingle | QA Mathematics Chooi, W. L. Lim, M. H. Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title | Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title_full | Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title_fullStr | Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title_full_unstemmed | Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title_short | Rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| title_sort | rank-one nonincreasing mappings on triangular matrices and some related preserver problems |
| topic | QA Mathematics |
| url | http://shdl.mmu.edu.my/2703/ http://shdl.mmu.edu.my/2703/ http://shdl.mmu.edu.my/2703/ |