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A Note on Linear Preservers of a Certain Matrix Partial Order

In: Formal Power Series and Algebraic Combinatorics

Author

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  • Alexander Guterman

    (Moscow State University, Department of Higher Algebra, Faculty of Mathematics and Mechanics)

Abstract

Let S be a semigroup. There is a fundamental relation that can be defined on the set of idempotents of S, if any. It is a well-known standard partial order, see [3, vol. 1, p. 23]: 1.1 $$e \leq f\;if\;and\;only\;if\;e = ef = fe.$$

Suggested Citation

  • Alexander Guterman, 2000. "A Note on Linear Preservers of a Certain Matrix Partial Order," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 441-446, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_40
    DOI: 10.1007/978-3-662-04166-6_40
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