Maps on matrix algebras preserving idempotents
โ Scribed by Gregor Dolinar
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 115 KB
- Volume
- 371
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
โฆ Synopsis
Let M n be the algebra of all n ร n complex matrices and P n the set of all idempotents in M n . Suppose ฯ : M n โ M n is a surjective map satisfying A -ฮปB โ P n if and only if
๐ SIMILAR VOLUMES
Let R be a commutative principal ideal domain, T : Mn(R) --\* Mm(R) an R-linear map which preserves idempotence. We determine the forms of T when n >/m and R ~ Fz, and solve some of Beasley's open problems. As a consequence, we prove that the set -~(R) of all R-linear maps on Mn(R) which preserve bo
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