Abstract:
Let Gn(Z) be the subsemigroup of GLn(Z) consisting of the matrices with nonnegative integer coefficients. In the paper, the automorphisms of this semigroup are described for n⩾2.
Bibliography: 5 titles.
Keywords:
matrices with nonnegative coefficients, automorphisms, integers.
\Bibitem{Sem12}
\by P.~P.~Semenov
\paper Automorphisms of semigroups of invertible matrices with nonnegative integer elements
\jour Sb. Math.
\yr 2012
\vol 203
\issue 9
\pages 1342--1356
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https://doi.org/10.1070/SM2012v203n09ABEH004267
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This publication is cited in the following 9 articles:
E. Bunina, K. Sosov, “Endomorphisms of the semigroup of nonnegative invertible matrices of order two over commutative ordered rings”, J. Math. Sci., 269:4 (2023), 469–478
V. V. Nemiro, “Endomorphisms of semigroups of invertible nonnegative matrices over ordered associative rings”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 75:5 (2020), 181–187
V. V. Nemiro, “The group of quotients of the semigroup of invertible nonnegative matrices over local rings”, J. Math. Sci., 257:6 (2021), 860–875
E. I. Bunina, A. V. Mikhalev, V. V. Nemiro, “Quotient groups of semigroups of invertible nonnegative matrices over skew fields”, Dokl. Math., 95:1 (2017), 12–14
E. I. Bunina, A. V. Mikhalev, V. V. Nemiro, “Groups of quotients of semigroups of invertible nonnegative matrices over skewfields”, J. Math. Sci., 233:5 (2018), 640–645
O. I. Tsarkov, “Endomorphisms of the semigroup $G_2(R)$ over partially ordered commutative rings without zero divisors and with $1/2$”, J. Math. Sci., 201:4 (2014), 534–551
E. I. Bunina, V. V. Nemiro, “The group of fractions of the semigroup of invertible nonnegative matrices of order three over a field”, J. Math. Sci., 206:5 (2015), 474–485
O. I. Tsarkov, “Extension of endomorphisms of the subsemigroup $\mathrm{GE}^+_2(R)$ to endomorphisms of $\mathrm{GE}^+_2(R[x])$, where $R$ is a partially-ordered commutative ring without zero divisors”, J. Math. Sci., 206:6 (2015), 711–733
P. P. Semenov, “Endomorphisms of semigroups of invertible nonnegative matrices over ordered rings”, J. Math. Sci., 193:4 (2013), 591–600
Citation in format AMSBIB
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