Let R be a commutative principal ideal domain, T: M-n(R) --> M-m(R) an R-linear map which preserves idempotence. We determine the forms of T when n greater than or equal to m and R not equal F-2, and solve some of Beasley's open problems. As a consequence, we prove that the set G(R) of all R-linear maps on M-n(R) which preserve both idempotence and nonidempotence is a proper subset of F(R), the set of all linear maps on M-n(R) that preserve idempotence, when the characteristic of R is 2. (C) Elsevier Science Inc., 1997. [References: 4]
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