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Krylov, Piotr Andreevich

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Total publications: 50
Scientific articles: 44

Number of views:
This page:6609
Abstract pages:15377
Full texts:3271
References:1135
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

http://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
2019
1. P. A. Krylov, A. A. Tuganbaev, “Automorphism groups of formal matrix rings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 164 (2019),  96–124  mathnet
2. P. A. Krylov, A. A. Tuganbaev, “Modules over discrete valuation domains. III”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 164 (2019),  74–95  mathnet
3. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “E-groups and E-rings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  111–132  mathnet
4. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “sp-Groups and their endomorphism rings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  68–110  mathnet
5. P. A. Krylov, A. A. Tuganbaev, A. V. Tsarev, “Around Baer–Kaplansky theorem”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 159 (2019),  46–67  mathnet
2018
6. 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
7. P. A. Krylov, T. D. Norbosambuev, “Group of automorphisms of one class of formal matrix algebras”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2018, 53,  16–21  mathnet  elib
2015
8. 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
9. 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
10. 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
2014
11. 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
12. 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
2013
13. 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
2011
14. I. A. Aleksandrov, P. A. Krylov, “Molin, scientist and educationalist”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, 3(15),  6–11  mathnet
2010
15. 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
16. 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
17. 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
18. 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
2009
19. 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
2008
20. 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
21. 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
2007
22. 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
23. P. A. Krylov, “The radicals of endomorphism rings of Abelian groups”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2007, 1,  17–27  mathnet  elib
2004
24. 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
25. 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
26. 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
2001
27. 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
28. 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, 4,  16–23  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 45:4 (2001), 14–21
29. 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
30. 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
2000
31. P. A. Krylov, “Mixed Abelian groups as modules over their endomorphism rings”, Fundam. Prikl. Mat., 6:3 (2000),  793–812  mathnet  mathscinet  zmath
1999
32. 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
1998
33. 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
1994
34. P. A. Krylov, “When is the extension group $Ext(A,B)$ torsion-free?”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, 10,  33–41  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 38:10 (1994), 29–37
35. 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
1991
36. P. A. Krylov, “Direct sums of strongly homogeneous abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 2,  65–68  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:2 (1991), 75–78
1990
37. 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
1989
38. 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
1987
39. P. A. Krylov, “Endogenerating abelian groups”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, 12,  52–55  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 31:12 (1987), 66–70
1979
40. P. A. Krylov, “Abelian torsion-free groups and their rings of endomorphisms”, Izv. Vyssh. Uchebn. Zaved. Mat., 1979, 11,  26–33  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 23:11 (1979), 25–33
1976
41. P. A. Krylov, “Sums of automorphisms of abelian groups, and the Jacobson radical of the endomorphism ring”, Izv. Vyssh. Uchebn. Zaved. Mat., 1976, 4,  56–66  mathnet  mathscinet  zmath
42. 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
1974
43. 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
1973
44. 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

2019
45. 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
46. P. A. Krylov, A. R. Chekhlov, “To the 110th anniversary of Sergei Antonovich Chunikhin”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2016, 1(39),  115–124  mathnet  elib
2012
47. P. A. Krylov, A. R. Chekhlov, “Grinshpon Samuil Yakovlevich (on the occasion of the 65th anniversary)”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2012, 4(20),  131–134  mathnet
48. 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, 3(19),  107–112  mathnet
2011
49. S. Ya. Grinshpon, P. A. Krylov, “Заметки об истории кафедры алгебры Томского государственного университета”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011, 3(15),  127–138  mathnet
2008
50. P. A. Krylov, “Mishina Anna Petrovna”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2008, 1(2),  97–99  mathnet

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