Affiliation:
1. School of Mathematical Science, Heilongjiang University, Harbin 150080, China
Abstract
SupposeFis an arbitrary field. Let|F|be the number of the elements ofF. LetMn(F)be the space of alln×nmatrices overF, letSn(F)be the subset ofMn(F)consisting of all symmetric matrices, and letTn(F)be the subset ofMn(F)consisting of all upper-triangular matrices. LetV∈{Sn(F),Mn(F),Tn(F)}; a mapΦ:V→Vis said to preserve idempotence ifA-λBis idempotent if and only ifΦ(A)-λΦ(B)is idempotent for anyA,B∈Vandλ∈F. In this paper, the maps preserving idempotence onSn(F),Mn(F), andTn(F)were characterized in case|F|=3.
Funder
Heilongjiang Education Committee