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Krylov, Piotr Andreevich
Statistics Math-Net.Ru
Total publications: 60
Scientific articles: 53

Number of views:
This page:10203
Abstract pages:25079
Full texts:6554
References:2009
Professor
Doctor of physico-mathematical sciences (1991)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords: abelian groups, modules, endomorphism rings.

Subject:

Scientific interests are connected with the theory of endomorphism rings of abelian groups, abelian groups, with a large number of endomorphisms (fully transitive etc.), extension and homomorphism groups of abelian groups, and with some problems of the theory of rings and modules.

Biography

Graduated from Faculty of Mathematics and Mechanics of Tomsk State University (TSU) in 1971 (department of algebra). Ph.D. thesis was defended in 1975. Ph.Sci. thesis was defended in 1991. A list of my works contains more then 50 titles. Since 1997 I have led the research seminar at TSU on algebra.

IN 1996 I was awarded the prize of the Tomsk State University for a series of papers on the endomorphism rings of Abelian groups.
   
Main publications:
  1. Krylov P. A., “Silno odnorodnye abelevy gruppy bez krucheniya”, Sib. matem. zh., 24:2 (1983), 77–84  zmath
  2. Krylov P. A., “O dvukh problemakh, kasayuschikhsya grupp rasshirenii abelevykh grupp”, Matem. sb., 185:1 (1994), 73–94  mathnet  mathscinet  zmath
  3. Krylov P. A., “Smeshannye abelevy gruppy kak moduli nad svoimi koltsami endomorfizmov”, Fund. i prikl. matem., 6:3 (2000), 793–812  mathnet  mathscinet  zmath
  4. Krylov P. A., Chekhlov A. R., “Abelevy gruppy bez krucheniya s bolshim chislom endomorfizmov”, Algebra. Topologiya, Sbornik statei, Tr. IMM, 7, no. 2, 2001, 194–207  mathnet  mathscinet  zmath; Krylov P. A., Chekhlov A. R., “Torsion-free abelian groups with a large number of endomorphisms”, Proc. Steklov Inst. Math., 2001, suppl. 2, S156–S168  mathscinet  zmath
  5. Krylov P. A., “Affinnye gruppy modulei i ikh avtomorfizmy”, Algebra i logika, 40:1 (2001), 60–82  mathnet  mathscinet  zmath

https://www.mathnet.ru/eng/person17534
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/245083

Publications in Math-Net.Ru Citations
2024
1. P. A. Krylov, T. D. Norbosambuev, “On automorphisms and derivations of reduced incidence algebras and coalgebras”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2024, no. 90,  33–39  mathnet
2023
2. P. A. Krylov, A. Tuganbaev, “On realization and isomorphism problems for formal matrix rings”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 219 (2023),  39–43  mathnet
3. P. A. Krylov, A. Tuganbaev, “Automorphisms of matrix rings”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 219 (2023),  16–38  mathnet 1
4. I. V. Dudin, P. A. Krylov, “Tensor product of incidence algebras and group algebras”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2023, no. 84,  5–13  mathnet
2021
5. P. A. Krylov, Ts. D. Norbosambuev, “$k$-good formal matrix rings of infinite order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 6,  35–42  mathnet; Russian Math. (Iz. VUZ), 65:6 (2021), 29–35
2019
6. P. A. Krylov, A. A. Tuganbaev, “Automorphism groups of formal matrix rings”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 164 (2019),  96–124  mathnet  mathscinet 3
7. P. A. Krylov, A. A. Tuganbaev, “Modules over discrete valuation domains. III”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 164 (2019),  74–95  mathnet  mathscinet
8. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “E-groups and E-rings”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  111–132  mathnet  mathscinet; J. Math. Sci. (N. Y.), 256:4 (2021), 341–361 1
9. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “sp-Groups and their endomorphism rings”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  68–110  mathnet  mathscinet; J. Math. Sci. (N. Y.), 256:3 (2021), 299–340 1
10. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “Around Baer–Kaplansky theorem”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  46–67  mathnet  mathscinet; J. Math. Sci. (N. Y.), 256:3 (2021), 278–298 3
2018
11. P. A. Krylov, T. D. Norbosambuev, “Automorphisms of formal matrix algebras”, Sibirsk. Mat. Zh., 59:5 (2018),  1116–1127  mathnet  elib; Siberian Math. J., 59:5 (2018), 885–893  isi  scopus 12
12. P. A. Krylov, T. D. Norbosambuev, “Group of automorphisms of one class of formal matrix algebras”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2018, no. 53,  16–21  mathnet  elib 4
2015
13. P. A. Krylov, “Determinants of generalized matrices of order $2$”, Fundam. Prikl. Mat., 20:5 (2015),  95–112  mathnet  mathscinet; J. Math. Sci., 230:3 (2018), 414–427 2
14. E. V. Kaigorodov, P. A. Krylov, “On some classes of Hopfian Abelian groups and modules”, Fundam. Prikl. Mat., 20:5 (2015),  61–68  mathnet  mathscinet; J. Math. Sci., 230:3 (2018), 392–397 3
15. P. A. Krylov, A. A. Tuganbaev, “Grothendieck and Whitehead groups of formal matrix rings”, Fundam. Prikl. Mat., 20:1 (2015),  173–203  mathnet  mathscinet  elib; J. Math. Sci., 223:5 (2017), 606–628 2
2014
16. P. A. Krylov, A. A. Tuganbaev, “Formal matrices and their determinants”, Fundam. Prikl. Mat., 19:1 (2014),  65–119  mathnet  mathscinet; J. Math. Sci., 211:3 (2015), 341–380  scopus 16
17. P. A. Krylov, “Calculation of the group $K_1$ of a generalized matrix ring”, Sibirsk. Mat. Zh., 55:4 (2014),  783–789  mathnet  mathscinet; Siberian Math. J., 55:4 (2014), 639–644  isi  scopus 5
2013
18. P. A. Krylov, “The group $K_0$ of a generalized matrix ring”, Algebra Logika, 52:3 (2013),  370–385  mathnet  mathscinet; Algebra and Logic, 52:3 (2013), 250–261  isi 7
2011
19. I. A. Aleksandrov, P. A. Krylov, “Molin, scientist and educationalist”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, no. 3(15),  6–11  mathnet 3
2010
20. P. A. Krylov, A. A. Tuganbaev, “Colocalizations and dualities for modules and Abelian groups”, Fundam. Prikl. Mat., 16:7 (2010),  161–180  mathnet  mathscinet; J. Math. Sci., 183:3 (2012), 383–396  scopus
21. P. A. Krylov, A. A. Tuganbaev, “Idempotent functors and localizations in categories of modules and Abelian groups”, Fundam. Prikl. Mat., 16:7 (2010),  75–159  mathnet  mathscinet; J. Math. Sci., 183:3 (2012), 323–382  scopus 5
22. O. M. Babanskaya (Katerinchuk), P. A. Krylov, “On a property of Abelian groups related to direct sums and products”, Fundam. Prikl. Mat., 16:7 (2010),  39–47  mathnet  mathscinet; J. Math. Sci., 183:3 (2012), 299–304  scopus
23. P. A. Krylov, “Injective modules over formal matrix rings”, Sibirsk. Mat. Zh., 51:1 (2010),  90–97  mathnet  mathscinet; Siberian Math. J., 51:1 (2010), 72–77  isi  scopus 7
2009
24. P. A. Krylov, A. A. Tuganbaev, “Modules over formal matrix rings”, Fundam. Prikl. Mat., 15:8 (2009),  145–211  mathnet  mathscinet  elib; J. Math. Sci., 171:2 (2010), 248–295  scopus 45
2008
25. P. A. Krylov, “Isomorphism of generalized matrix rings”, Algebra Logika, 47:4 (2008),  456–463  mathnet  mathscinet  zmath; Algebra and Logic, 47:4 (2008), 258–262  isi  scopus 60
26. P. A. Krylov, E. Yu. Yardykov, “Projective and hereditary modules over generalized matrix ring”, Fundam. Prikl. Mat., 14:5 (2008),  125–138  mathnet  mathscinet; J. Math. Sci., 163:6 (2009), 709–719  scopus 2
2007
27. P. A. Krylov, Y. I. Podberezina, “The group $\operatorname{Hom}(A,B)$ as an Artinian $\operatorname{E}(B)$- or $\operatorname{E}(A)$-module”, Fundam. Prikl. Mat., 13:3 (2007),  81–96  mathnet  mathscinet  zmath; J. Math. Sci., 154:3 (2008), 333–343  scopus 3
28. P. A. Krylov, “The radicals of endomorphism rings of Abelian groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2007, no. 1,  17–27  mathnet  elib 3
2004
29. P. A. Krylov, “The Jacobson Radical of an Endomorphism Ring for an Abelian Group”, Algebra Logika, 43:1 (2004),  60–76  mathnet  mathscinet  zmath  elib; Algebra and Logic, 43:1 (2004), 34–43  elib  scopus 12
30. P. A. Krylov, E. G. Pakhomova, “When Is the Group $\operatorname{Hom}(A,B)$ an Injective $E(B)$-Module?”, Mat. Zametki, 75:1 (2004),  100–108  mathnet  mathscinet  zmath; Math. Notes, 75:1 (2004), 93–100  isi
2002
31. P. A. Krylov, “Hereditary endomorphism rings of mixed Abelian groups”, Sibirsk. Mat. Zh., 43:1 (2002),  108–119  mathnet  mathscinet  zmath; Siberian Math. J., 43:1 (2002), 83–91  isi 13
2001
32. P. A. Krylov, “Affine Module Groups and Their Automorphisms”, Algebra Logika, 40:1 (2001),  60–82  mathnet  mathscinet  zmath; Algebra and Logic, 40:1 (2001), 34–46  scopus 11
33. M. V. Eremina, P. A. Krylov, “The tensor product of abelian groups as a Noetherian module over an endomorphism ring”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 4,  16–23  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 45:4 (2001), 14–21 4
34. P. A. Krylov, E. G. Pakhomova, “Abelian Groups and Regular Modules”, Mat. Zametki, 69:3 (2001),  402–411  mathnet  mathscinet  zmath; Math. Notes, 69:3 (2001), 364–372  isi 15
35. P. A. Krylov, A. R. Chekhlov, “Torsion-free abelian groups with a large number of endomorphisms”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:2 (2001),  194–207  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 2, S156–S168 7
2000
36. P. A. Krylov, “Mixed Abelian groups as modules over their endomorphism rings”, Fundam. Prikl. Mat., 6:3 (2000),  793–812  mathnet  mathscinet  zmath 17
1999
37. P. A. Krylov, E. D. Klassen, “The center of the endomorphism ring of a split mixed abelian group”, Sibirsk. Mat. Zh., 40:5 (1999),  1074–1085  mathnet  mathscinet  zmath; Siberian Math. J., 40:5 (1999), 907–916  isi 12
1998
38. P. A. Krylov, E. G. Pakhomova, “Abelian groups as injective modules over endomorphism rings”, Fundam. Prikl. Mat., 4:4 (1998),  1365–1384  mathnet  mathscinet  zmath 5
1994
39. P. A. Krylov, “When is the extension group $Ext(A,B)$ torsion-free?”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 10,  33–41  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:10 (1994), 29–37 1
40. P. A. Krylov, “On two problems concerning extension groups of Abelian groups”, Mat. Sb., 185:1 (1994),  73–94  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 81:1 (1995), 59–76  isi 3
1991
41. P. A. Krylov, “Direct sums of strongly homogeneous abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 2,  65–68  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:2 (1991), 75–78 1
1990
42. P. A. Krylov, “Completely transitive torsion-free abelian groups”, Algebra Logika, 29:5 (1990),  549–560  mathnet  mathscinet 15
43. P. A. Krylov, “On modules with complete rings of endomorphisms”, Uspekhi Mat. Nauk, 45:4(274) (1990),  159–160  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:4 (1990), 177–178  isi 2
1989
44. P. A. Krylov, “A class of quasipure injective Abelian groups”, Mat. Zametki, 45:4 (1989),  53–58  mathnet  mathscinet  zmath; Math. Notes, 45:4 (1989), 301–304  isi 1
1988
45. P. A. Krylov, “Torsion-free abelian groups with hereditary endomorphism rings”, Algebra Logika, 27:3 (1988),  295–304  mathnet  mathscinet 1
1987
46. P. A. Krylov, “Endogenerating abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 12,  52–55  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 31:12 (1987), 66–70
47. P. A. Krylov, “A class of abelian groups with hereditary endomorphism rings”, Sibirsk. Mat. Zh., 28:6 (1987),  60–65  mathnet  mathscinet  zmath; Siberian Math. J., 28:6 (1987), 912–916  isi
1983
48. P. A. Krylov, “Strongly homogeneous torsion-free abelian groups”, Sibirsk. Mat. Zh., 24:2 (1983),  77–84  mathnet  mathscinet  zmath; Siberian Math. J., 24:2 (1983), 215–221  isi 19
1979
49. P. A. Krylov, “Abelian torsion-free groups and their rings of endomorphisms”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, no. 11,  26–33  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 23:11 (1979), 25–33 2
1976
50. P. A. Krylov, “Sums of automorphisms of abelian groups, and the Jacobson radical of the endomorphism ring”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, no. 4,  56–66  mathnet  mathscinet  zmath 5
51. P. A. Krylov, “Torsion-free Abelian groups with cyclic $p$-basic subgroups”, Mat. Zametki, 20:6 (1976),  805–813  mathnet  mathscinet  zmath; Math. Notes, 20:6 (1976), 1011–1015 1
1974
52. P. A. Krylov, “Radicals of endomorphism rings of torsion-free Abelian groups”, Mat. Sb. (N.S.), 95(137):2(10) (1974),  214–228  mathnet  mathscinet  zmath; Math. USSR-Sb., 24:2 (1974), 209–222 10
1973
53. P. A. Krylov, “Extension of isomorphisms in abelian $p$-groups”, Mat. Zametki, 14:4 (1973),  543–548  mathnet  mathscinet  zmath; Math. Notes, 14:4 (1973), 870–872 2
2024
54. A. A. Fomin, A. Tuganbaev, P. A. Krylov, E. A. Timoshenko, A. V. Tsarev, E. V. Kaygorodov, Ts. D. Norbosambuev, “Andrey Rostislavovich Chekhlov (to the 65th anniversary of his birth)”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2024, no. 88,  179–185  mathnet
2019
55. V. N. Chubarikov, N. M. Dobrovolsky, V. A. Artamonov, A. V. Mikhalev, V. N. Latyshev, Yu. V. Nesterenko, A. Ya. Belov, A. V. Grishin, E. I. Kompantseva, A. V. Tsarev, E. I. Deza, P. A. Krylov, A. A. Tuganbaev, “Alexander Alexandrovich Fomin (to the 70th anniversary)”, Chebyshevskii Sb., 20:2 (2019),  579–582  mathnet
2016
56. P. A. Krylov, A. R. Chekhlov, “To the 110th anniversary of Sergei Antonovich Chunikhin”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2016, no. 1(39),  115–124  mathnet  elib
2012
57. P. A. Krylov, A. R. Chekhlov, “Grinshpon Samuil Yakovlevich (on the occasion of the 65th anniversary)”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, no. 4(20),  131–134  mathnet
58. P. A. Krylov, A. R. Chekhlov, “The first head of the Department of Algebra in Tomsk State University”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, no. 3(19),  107–112  mathnet 1
2011
59. S. Ya. Grinshpon, P. A. Krylov, “Заметки об истории кафедры алгебры Томского государственного университета”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, no. 3(15),  127–138  mathnet 4
2008
60. P. A. Krylov, “Mishina Anna Petrovna”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2008, no. 1(2),  97–99  mathnet

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