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Algebra Logika, 2008, Volume 47, Number 4, Pages 456–463 (Mi al367)  

This article is cited in 30 scientific papers (total in 30 papers)

Isomorphism of generalized matrix rings

P. A. Krylov


Abstract: An isomorphism problem is considered for generalized matrix rings with values in a given ring $R$. An exhaustive answer is given for the case of a commutative domain $R$ and a commutative local ring $R$.

Keywords: generalized matrix ring, central element, isomorphism.

Full text: PDF file (135 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2008, 47:4, 258–262

Bibliographic databases:

UDC: 512.55
Received: 13.03.2008

Citation: P. A. Krylov, “Isomorphism of generalized matrix rings”, Algebra Logika, 47:4 (2008), 456–463; Algebra and Logic, 47:4 (2008), 258–262

Citation in format AMSBIB
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\by P.~A.~Krylov
\paper Isomorphism of generalized matrix rings
\jour Algebra Logika
\yr 2008
\vol 47
\issue 4
\pages 456--463
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\transl
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 4
\pages 258--262
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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. P. A. Krylov, A. A. Tuganbaev, “Modules over formal matrix rings”, J. Math. Sci., 171:2 (2010), 248–295  mathnet  crossref  mathscinet  elib
    2. Xiao Zhankui, Wei Feng, “Commuting mappings of generalized matrix algebras”, Linear Algebra Appl., 433:11-12 (2010), 2178–2197  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. V. Budanov, “Ideals of generalized matrix rings”, Sb. Math., 202:1 (2011), 1–8  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Tang G., Zhou Y., “Strong Cleanness of Generalized Matrix Rings Over a Local Ring”, Linear Alg. Appl., 437:10 (2012), 2546–2559  crossref  mathscinet  zmath  isi  elib  scopus
    5. Li Ya., Wei F., “Semi-Centralizing Maps of Generalized Matrix Algebras”, Linear Alg. Appl., 436:5 (2012), 1122–1153  crossref  mathscinet  zmath  isi  elib  scopus
    6. Tang G., Zhou Y., “A Class of Formal Matrix Rings”, Linear Alg. Appl., 438:12 (2013), 4672–4688  crossref  mathscinet  zmath  isi  elib  scopus
    7. P. A. Krylov, “The group $K_0$ of a generalized matrix ring”, Algebra and Logic, 52:3 (2013), 250–261  mathnet  crossref  mathscinet  isi
    8. P. A. Krylov, “Calculation of the group $K_1$ of a generalized matrix ring”, Siberian Math. J., 55:4 (2014), 639–644  mathnet  crossref  mathscinet  isi
    9. Tang G., Li Ch., Zhou Y., “Study of Morita Contexts”, Commun. Algebr., 42:4 (2014), 1668–1681  crossref  mathscinet  zmath  isi  elib  scopus
    10. P. A. Krylov, A. A. Tuganbaev, “Formal matrices and their determinants”, J. Math. Sci., 211:3 (2015), 341–380  mathnet  crossref  mathscinet
    11. Huang Q., Tang G., Zhou Y., “Quasipolar Property of Generalized Matrix Rings”, Commun. Algebr., 42:9 (2014), 3883–3894  crossref  mathscinet  zmath  isi  elib  scopus
    12. Xiao Zh., Wei F., “Commuting Traces and Lie Isomorphisms on Generalized Matrix Algebras”, Oper. Matrices, 8:3 (2014), 821–847  crossref  mathscinet  zmath  isi
    13. A. N. Abyzov, D. T. Tapkin, “On certain classes of rings of formal matrices”, Russian Math. (Iz. VUZ), 59:3 (2015), 1–12  mathnet  crossref
    14. A. N. Abyzov, “Rings of formal matrices close to regular ones”, Russian Math. (Iz. VUZ), 59:10 (2015), 49–52  mathnet  crossref
    15. D. T. Tapkin, “Koltsa formalnykh matrits i obobschenie algebry intsidentnosti”, Chebyshevskii sb., 16:3 (2015), 422–449  mathnet  elib
    16. A. N. Abyzov, D. T. Tapkin, “Formal matrix rings and their isomorphisms”, Siberian Math. J., 56:6 (2015), 955–967  mathnet  crossref  crossref  mathscinet  isi  elib
    17. P. A. Krylov, A. A. Tuganbaev, “Grothendieck and Whitehead groups of formal matrix rings”, J. Math. Sci., 223:5 (2017), 606–628  mathnet  crossref  mathscinet  elib
    18. Liang X. Wei F. Xiao Zh. Fosner A., “Centralizing Traces and Lie Triple Isomorphisms on Generalized Matrix Algebras”, Linear Multilinear Algebra, 63:9 (2015), 1786–1816  crossref  mathscinet  zmath  isi  elib  scopus
    19. P. A. Krylov, “Determinants of generalized matrices of order $2$”, J. Math. Sci., 230:3 (2018), 414–427  mathnet  crossref  mathscinet
    20. Kosan M.T., Wang Zh., Zhou Y., “Nil-Clean and Strongly Nil-Clean Rings”, J. Pure Appl. Algebr., 220:2 (2016), 633–646  crossref  mathscinet  zmath  isi  elib  scopus
    21. Han D., Wei F., “Multiplicative Lie Higher Derivations of Unital Algebras With Idempotents”, Oper. Matrices, 10:2 (2016), 345–377  crossref  mathscinet  zmath  isi  scopus
    22. A. N. Abyzov, A. A. Tuganbaev, “Formal matrices and rings close to regular”, J. Math. Sci., 233:5 (2018), 604–615  mathnet  crossref
    23. D. T. Tapkin, “Isomorphisms of formal matrix incidence rings”, Russian Math. (Iz. VUZ), 61:12 (2017), 73–79  mathnet  crossref  isi
    24. Kurtulmaz Y., “Very Cleanness of Generalized Matrices”, Bull. Iran Math. Soc., 43:5 (2017), 1457–1465  mathscinet  isi
    25. Calci M.B., Chen H., Halicioglu S., Harmanci A., “Reversibility of Rings With Respect to the Jacobson Radical”, Mediterr. J. Math., 14:3 (2017), UNSP 137  crossref  mathscinet  isi  scopus
    26. Krylov P., Tuganbaev A., “Formal Matrices”, Formal Matrices, Algebra and Applications, 23, Springer International Publishing Ag, 2017, 1–156  crossref  mathscinet  isi
    27. P. A. Krylov, Ts. D. Norbosambuev, “Gruppa avtomorfizmov odnogo klassa algebr formalnykh matrits”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 53, 16–21  mathnet  crossref  elib
    28. D. T. Tapkin, “Isomorphisms of formal matrix rings with zero trace ideals”, Siberian Math. J., 59:3 (2018), 523–535  mathnet  crossref  crossref  isi  elib
    29. P. A. Krylov, T. D. Norbosambuev, “Automorphisms of formal matrix algebras”, Siberian Math. J., 59:5 (2018), 885–893  mathnet  crossref  crossref  isi
    30. Gurgun O., Halicioglu S., Harmanci A., “Quasipolarity of Special Morita Context Rings”, Miskolc Math. Notes, 19:1 (2018), 273–289  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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