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Journal of Mathematics
Volume 2015, Article ID 428203, 6 pages
http://dx.doi.org/10.1155/2015/428203
Research Article

Maps Preserving Idempotence on Matrix Spaces

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 5 July 2015; Accepted 30 August 2015

Academic Editor: Fernando Torres

Copyright © 2015 Yuqiu Sheng and Hanyu Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose is an arbitrary field. Let be the number of the elements of . Let be the space of all matrices over , let be the subset of consisting of all symmetric matrices, and let be the subset of consisting of all upper-triangular matrices. Let ; a map is said to preserve idempotence if is idempotent if and only if is idempotent for any and . In this paper, the maps preserving idempotence on , , and were characterized in case .