Linear maps preserving idempotence on matrix modules over principal ideal domains

✍ Scribed by Liu Shaowu

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 379 KB
• Volume: 258
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00203-0

✦ Synopsis

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 both idempotence and nonidempotence is a proper subset of ~r(R), the set of all linear maps on Mn(R) that preserve idempotence, when the characteristic of R is 2.