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Maps Preserving Idempotence on Matrix Spaces

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  • Yuqiu Sheng
  • Hanyu Zhang

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 .

Suggested Citation

  • Yuqiu Sheng & Hanyu Zhang, 2015. "Maps Preserving Idempotence on Matrix Spaces," Journal of Mathematics, Hindawi, vol. 2015, pages 1-6, September.
    • Handle: RePEc:hin:jjmath:428203
    DOI: 10.1155/2015/428203
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