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Fundam. Prikl. Mat., 2008, Volume 14, Issue 4, Pages 75–85 (Mi fpm1126)  

This article is cited in 6 scientific papers (total in 6 papers)

Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings

E. I. Bunina, P. P. Semenov

M. V. Lomonosov Moscow State University

Abstract: In the paper we prove that if two semigroups of invertible matrices with nonnegative elements over partially ordered commutative rings are elementarily equivalent, then their dimensions coincide and the corresponding semirings of nonnegative elements are elementarily equivalent.

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English version:
Journal of Mathematical Sciences (New York), 2009, 163:5, 493–499

Bibliographic databases:

UDC: 512.534.7+510.67

Citation: E. I. Bunina, P. P. Semenov, “Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings”, Fundam. Prikl. Mat., 14:4 (2008), 75–85; J. Math. Sci., 163:5 (2009), 493–499

Citation in format AMSBIB
\Bibitem{BunSem08}
\by E.~I.~Bunina, P.~P.~Semenov
\paper Elementary equivalence of semigroups of invertible matrices with nonnegative elements over commutative partially ordered rings
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 4
\pages 75--85
\mathnet{http://mi.mathnet.ru/fpm1126}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2482034}
\elib{http://elibrary.ru/item.asp?id=12174971}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 163
\issue 5
\pages 493--499
\crossref{https://doi.org/10.1007/s10958-009-9687-5}
\elib{http://elibrary.ru/item.asp?id=15312441}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70649113047}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. P. Semenov, “Automorphisms of semigroups of invertible matrices with nonnegative integer elements”, Sb. Math., 203:9 (2012), 1342–1356  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. P. P. Semenov, “Endomorphisms of semigroups of invertible nonnegative matrices over ordered rings”, J. Math. Sci., 193:4 (2013), 591–600  mathnet  crossref
    3. 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  mathnet  crossref  mathscinet
    4. 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  mathnet  crossref  mathscinet
    5. 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  mathnet  crossref  mathscinet
    6. 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  mathnet  crossref
  • Фундаментальная и прикладная математика
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