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The group of commutativity preserving maps on strictly upper triangular matrices
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Dengyin Rou, Jianling |
| Copyright Year | 2014 |
| Abstract | Let N = Nn(R) be the algebra of all n × n strictly upper triangular matrices over a unital commutative ring R. A map φ on N is called preserving commutativity in both directions if xy = yx ⇔ φ(x)φ(y) = φ(y)φ(x). In this paper, we prove that each invertible linear map on N preserving commutativity in both directions is exactly a quasi-automorphism of N, and a quasi-automorphism of N can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings. |
| Starting Page | 335 |
| Ending Page | 350 |
| Page Count | 16 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10587-014-0105-x |
| Volume Number | 64 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s10587-014-0105-x |
| Alternate Webpage(s) | https://doi.org/10.1007/s10587-014-0105-x |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
