Abstract
In this paper, we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly ordered associative ring on some specially defined subgroup coincides with the composition of an inner automorphism of the semigroup, an order-preserving automorphism of the ring, and a central homothety.
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References
S. N. Ilyin, “Invertible matrices over (nonassociative) antirings,” in: Universal Algebra and Its Applications [in Russian], Peremena, Volgograd (2000), pp. 81–89.
A. V. Mikhalev and M. A. Shatalova, “Automorphisms and antiautomorphisms of the semigroup of invertible matrices with nonnegative elements,” Mat. Sb., 81(123), No. 4, 600–609 (1970).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 3–23, 2005.
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Bunina, E.I., Mikhalev, A.V. Automorphisms of the semigroup of invertible matrices with nonnegative elements. J Math Sci 142, 1867–1882 (2007). https://doi.org/10.1007/s10958-007-0094-5
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DOI: https://doi.org/10.1007/s10958-007-0094-5