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Funktsional. Anal. i Prilozhen., 1991, Volume 25, Issue 2, Pages 13–25 (Mi faa856)  

This article is cited in 20 scientific papers (total in 20 papers)

Determinants of matrices over noncommutative rings

I. M. Gel'fand, V. S. Retakh

Scientific Research Institute for System Studies, USSR Academy of Sciences

Full text: PDF file (1492 kB)
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English version:
Functional Analysis and Its Applications, 1991, 25:2, 91–102

Bibliographic databases:

UDC: 512.55
Received: 10.11.1990

Citation: I. M. Gel'fand, V. S. Retakh, “Determinants of matrices over noncommutative rings”, Funktsional. Anal. i Prilozhen., 25:2 (1991), 13–25; Funct. Anal. Appl., 25:2 (1991), 91–102

Citation in format AMSBIB
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\by I.~M.~Gel'fand, V.~S.~Retakh
\paper Determinants of matrices over noncommutative rings
\jour Funktsional. Anal. i Prilozhen.
\yr 1991
\vol 25
\issue 2
\pages 13--25
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\transl
\jour Funct. Anal. Appl.
\yr 1991
\vol 25
\issue 2
\pages 91--102
\crossref{https://doi.org/10.1007/BF01079588}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. M. Gel'fand, V. S. Retakh, “A theory of noncommutative determinants and characteristic functions of graphs”, Funct. Anal. Appl., 26:4 (1992), 231–246  mathnet  crossref  mathscinet  zmath  isi
    2. A. N. Leznov, “Graded Lie algebras, representation theory, integrable mappings, and integrable systems”, Theoret. and Math. Phys., 122:2 (2000), 211–228  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. M. Goncharenko, “Monodromy of the matrix Schrödinger equations and interaction of matrix solitons”, Russian Math. Surveys, 55:5 (2000), 995–997  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. M. Goncharenko, “Multisoliton Solutions of the Matrix KdV Equation”, Theoret. and Math. Phys., 126:1 (2001), 81–91  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Mark J. Hopkins, Alexander I. Molev, “A $q$-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra”, SIGMA, 2 (2006), 092, 29 pp.  mathnet  crossref  mathscinet  zmath
    6. I. I. Kirchei, “Cramer's rule for quaternionic systems of linear equations”, J. Math. Sci., 155:6 (2008), 839–858  mathnet  crossref  mathscinet  zmath  elib
    7. Chervov, A, “Algebraic properties of Manin matrices 1”, Advances in Applied Mathematics, 43:3 (2009), 239  crossref  mathscinet  zmath  isi
    8. Gilson, CR, “Dromion solutions of noncommutative Davey-Stewartson equations”, Journal of Physics A-Mathematical and Theoretical, 42:23 (2009), 235202  crossref  mathscinet  zmath  adsnasa  isi
    9. Poplavskii V.B., “Ob opredelitelyakh matrits nad polyami, koltsami i polukoltsami”, Vestnik Moskovskoi gosudarstvennoi akademii delovogo administrirovaniya. Seriya: Filosofskie, sotsialnye i estestvennye nauki, 2011, no. 5, 158–165  elib
    10. A. M. Galmak, “Vektor-opredeliteli i opredeliteli vektor-matrits”, PFMT, 2011, no. 2(7), 58–64  mathnet
    11. Bushra Haider, Mahmood-ul Hassan, “Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System”, SIGMA, 8 (2012), 084, 15 pp.  mathnet  crossref  mathscinet
    12. G. P. Egorychev, “Novye polinomialnye tozhdestva dlya determinantov nad kommutativnymi koltsami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:4 (2012), 16–20  mathnet
    13. Egorychev G.P., “Novoe semeistvo polinomialnykh tozhdestv dlya vychisleniya determinantov”, Doklady akademii nauk, 452:1 (2013), 14–14  crossref  mathscinet  zmath  elib
    14. Georgy P. Egorychev, “The determinants over associative rings: a definition, properties, new formulas and a computational complexity”, Zhurn. SFU. Ser. Matem. i fiz., 9:4 (2016), 443–448  mathnet  crossref
    15. H. Wajahat A. Riaz, M. Hassan, “Darboux transformation for a semidiscrete short-pulse equation”, Theoret. and Math. Phys., 194:3 (2018), 360–376  mathnet  crossref  crossref  isi  elib
    16. H. Wajahat A. Riaz, M. Hassan, “Generalized lattice Heisenberg magnet model and its quasideterminant soliton solutions”, Theoret. and Math. Phys., 195:2 (2018), 665–675  mathnet  crossref  crossref  adsnasa  isi  elib
    17. M. Hamanaka, H. Okabe, “Soliton scattering in noncommutative spaces”, Theoret. and Math. Phys., 197:1 (2018), 1451–1468  mathnet  crossref  crossref  adsnasa  isi  elib
    18. Bolsinov A. Matveev V.S. Miranda E. Tabachnikov S., “Open Problems, Questions and Challenges in Finite-Dimensional Integrable Systems”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 376:2131 (2018), 20170430  crossref  isi  scopus
    19. G. P. Egorychev, “Determinanty kak kombinatornye formuly summirovaniya nad algebroi s edinstvennoi $n$-arnoi operatsiei”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 121–127  mathnet  crossref
    20. Z. Amjad, B. Haider, “Binary Darboux transformations of the supersymmetric Heisenberg magnet model”, Theoret. and Math. Phys., 199:3 (2019), 784–797  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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