Balaba, Irina Nikolaevna

Statistics Math-Net.Ru
Total publications: 27
Scientific articles: 23
Presentations: 2

Number of views:
This page:1604
Abstract pages:6566
Full texts:2346
Associate professor
Doctor of physico-mathematical sciences (2012)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Keywords: graded rings and modules; Morita's theorems; density theorems; equivalence of categories of modules; radicals; superalgebras.
UDC: 512.55, 512.552, 512.554.36
MSC: 16W50, 16W20, 16S90, 17A70, 17B05, 18E40, 16N80, 16D80


The equivalence of rigid subcategories of categories of graded modules was studied, in particular, graded variant of Morita's theorem was obtained. The properties of graded maximal ring of quotients for semiprime ring graded by ordered group was studied. Some characterization of weakly primitive rings graded by semigroup was obtained. Modules are graded by acts with some cancellation conditions over these semigroups.


Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1980 and post graduated in 1983 (department of high algebra). Ph.D. thesis was defended in  2013. A list of my works contains about 100 titles.

Main publications:
  1. Balaba I. N., “O slabo primitivnykh graduirovannykh koltsakh”, UMN, 56:6 (2001), 139–140  mathnet  crossref  mathscinet
  2. Balaba I. N., “Ekvivalentnosti Mority kategorii graduirovannykh modulei”, UMN, 42:3 (1987), 177–178  mathnet  mathscinet
  3. Balaba I. N., “Refleksivnye graduirovannye moduli”, Sb.: Algoritmicheskie problemy teorii grupp i polugrupp, Tula, 1991, 88–96
  4. Balaba I. N., “Koltsa chastnykh polupervichnykh graduirovannykh kolets”, Sb. trudov mezhdunarodnoi konferentsii «Universalnaya algebra i ee prilozheniya», Volgograd, 2000, 21–28
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. N. N. Dobrovol'skii, M. N. Dobrovol'skii, N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, “Dirichlet series algebra of a monoid of natural numbers”, Chebyshevskii Sb., 20:1 (2019),  180–196  mathnet
2. N. N. Dobrovolsky, M. N. Dobrovolsky, N. M. Dobrovolsky, I. N. Balaba, I. Yu. Rebrova, “Hypothesis about "barier series" for the zeta-functions of monoids with the exponential sequence of primes”, Chebyshevskii Sb., 19:1 (2018),  106–123  mathnet  elib
3. S. S. Demidov, E. A. Morozova, V. N. Chubarikov, I. Yu. Rebrova, I. N. Balaba, N. N. Dobrovol'skii, N. M. Dobrovol'skii, L. P. Dobrovol'skaya, A. V. Rodionov, O. A. Pikhtil'kova, “Number-theoretic method in approximate analysis”, Chebyshevskii Sb., 18:4 (2017),  6–85  mathnet  elib
4. N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, N. N. Dobrovol'skii, E. A. Matveeva, “On fractional linear transformations of forms A. Thue–M. N. Dobrovolsky–V. D. Podsypanina”, Chebyshevskii Sb., 18:2 (2017),  54–97  mathnet  elib
5. N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, N. N. Dobrovol'skii, “On Lagrange algorithm for reduced algebraic irrationalities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, 2,  27–39  mathnet
6. I. N. Balaba, E. N. Krasnova, “Semisimple graded rings”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(2) (2013),  23–28  mathnet
7. I. N. Balaba, A. L. Kanunnikov, A. V. Mikhalev, “Quotient rings of graded associative rings. I”, Fundam. Prikl. Mat., 17:2 (2012),  3–74  mathnet; J. Math. Sci., 186:4 (2012), 531–577  scopus
8. I. N. Balaba, “Graded regular rings and modules”, Chebyshevskii Sb., 11:3 (2010),  22–31  mathnet  zmath
9. I. N. Balaba, V. A. Efremov, “Graded quotient rings of semiprime graded rings”, Chebyshevskii Sb., 11:1 (2010),  20–30  mathnet  mathscinet
10. I. N. Balaba, A. V. Mikhalev, “Isomorphisms and anti-isomorphisms of endomorphism rings of graded modules that are close to free ones”, Dokl. Akad. Nauk, 425:5 (2009),  583–586  mathnet  mathscinet  elib
11. I. N. Balaba, A. V. Mikhalev, “Anti-isomorphisms of graded endomorphism rings of graded modules close to free ones”, Fundam. Prikl. Mat., 14:7 (2008),  23–36  mathnet  mathscinet  elib; J. Math. Sci., 164:2 (2010), 168–177  scopus
12. I. N. Balaba, “Prime graded modules”, Fundam. Prikl. Mat., 14:4 (2008),  65–74  mathnet  mathscinet; J. Math. Sci., 163:5 (2009), 487–492  scopus
13. I. N. Balaba, “Inducibility of anti-isomorphisms of endomorphism rings of graded modules by anti-semilinear transformations”, Uspekhi Mat. Nauk, 63:3(381) (2008),  151–152  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:3 (2008), 551–553  isi  scopus
14. I. N. Balaba, A. V. Mikhalev, “Isomorphisms of graded endomorphism rings of graded modules close to free ones”, Fundam. Prikl. Mat., 13:5 (2007),  3–18  mathnet  mathscinet  zmath  elib; J. Math. Sci., 156:2 (2009), 209–218  elib  scopus
15. I. N. Balaba, “Isomorphisms of graded endomorphism rings of progenerators”, Fundam. Prikl. Mat., 13:1 (2007),  3–10  mathnet  mathscinet  zmath  elib; J. Math. Sci., 152:4 (2008), 451–455  elib  scopus
16. A. V. Mikhalev, I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of graded $\Omega$-groups”, Fundam. Prikl. Mat., 12:2 (2006),  159–174  mathnet  mathscinet  zmath  elib; J. Math. Sci., 149:2 (2008), 1146–1156  elib  scopus
17. I. N. Balaba, “Special radicals of graded rings”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, 1,  26–33  mathnet  mathscinet  zmath
18. I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of special Lie superalgebras”, Fundam. Prikl. Mat., 9:1 (2003),  51–60  mathnet  mathscinet  zmath  elib; J. Math. Sci., 128:6 (2005), 3365–3371  elib  scopus
19. I. N. Balaba, S. V. Zelenov, S. V. Limarenko, A. V. Mikhalev, “Density theorems for graded rings”, Fundam. Prikl. Mat., 9:1 (2003),  27–49  mathnet  mathscinet  zmath; J. Math. Sci., 128:6 (2005), 3350–3364  scopus
20. I. N. Balaba, “Graded prime PI-algebras”, Fundam. Prikl. Mat., 9:1 (2003),  19–26  mathnet  mathscinet  zmath  elib; J. Math. Sci., 128:6 (2005), 3345–3349  elib  scopus
21. I. N. Balaba, “Weakly primitive graded rings”, Uspekhi Mat. Nauk, 56:6(342) (2001),  139–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 56:6 (2001), 1153–1154  isi  scopus
22. I. N. Balaba, “Morita equivalences of categories of graded modules”, Uspekhi Mat. Nauk, 42:3(255) (1987),  177–178  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:3 (1987), 209–210  isi
23. I. N. Balaba, “Calculation of the dimension polynomial of a prime principal difference ideal”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, 2,  16–20  mathnet  mathscinet  zmath
24. I. N. Balaba, “Dimensional polynomials of extension of difference fields”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1984, 2,  31–35  mathnet  mathscinet  zmath

25. K. K. Andreev, G. N. Arzhantseva, V. A. Artamonov, V. S. Atabekyan, I. N. Balaba, N. V. Bezverkhny, A. A. Vdovina, V. S. Guba, A. E. Guterman, G. S. Deryabina, N. M. Dobrovolsky, M. V. Zaicev, A. L. Kanunnikov, A. A. Klyachko, O. V. Kulikova, O. V. Markova, V. H. Mikaelyan, M. V. Milentyeva, A. E. Minasyan, K. V. Mikhailovsky, A. V. Mikhalev, A. E. Pankratiev, Yu. G. Prokhorov, Yu. S. Semenov, D. A. Timashev, V. N. Chubarikov, I. A. Chubarov, E. E. Shirshova, “Alexander Yuryevich Olshanskii (to the 75th anniversary)”, Chebyshevskii Sb., 22:2 (2021),  347–365  mathnet
26. I. N. Balaba, E. I. Bunina, S. T. Glavatsky, I. B. Kozhukhov, “To the 80th anniversary of Alexander Vasilyevich Mikhalev”, Chebyshevskii Sb., 22:1 (2021),  8–26  mathnet
27. N. M. Adrianov, V. A. Artamonov, I. N. Balaba, Yu. A. Bahturin, L. A. Bokut', V. V. Borisenko, E. I. Bunina, S. A. Gaifullin, S. T. Glavatsky, I. Z. Golubchik, S. González, A. V. Grishin, A. È. Guterman, N. I. Dubrovin, M. V. Zaicev, E. I. Zel'manov, N. K. Il'ina, A. Ya. Kanel-Belov, A. L. Kanunnikov, E. S. Kislitsyn, A. A. Klyachko, I. B. Kozhukhov, E. M. Kreines, O. V. Kulikova, T. P. Lukashenko, O. V. Markova, C. Martínez, A. A. Mikhalev, A. V. Mikhalev, A. Yu. Ol'shanskii, A. E. Pentus, A. V.A. Petrov, Yu. G. Prokhorov, S. V. Pchelintsev, V. V. Tenzina, D. A. Timashev, A. A. Tuganbaev, I. N. Tumaikin, V. K. Kharchenko, I. A. Chubarov, A. A. Shafarevich, A. I. Shafarevich, I. P. Shestakov, E. E. Shirshova, V. É. Shpil'rain, “Viktor Timofeevich Markov (21.06.1948—15.07.2019)”, Fundam. Prikl. Mat., 23:2 (2020),  3–16  mathnet
28. V. A. Artamonov, V. N. Latyshev, O. A. Pikhtilkova, I. N. Balaba, N. M. Dobrovol'skii, I. V. Dobrynina, I. Yu. Rebrova, “Pikhtilkov Sergrey Alekseevich. The life and scientific activity”, Chebyshevskii Sb., 17:1 (2016),  299–309  mathnet  elib

Presentations in Math-Net.Ru
1. Graded division rings and modules over them
I. N. Balaba, A V. Mikhalev
XVI International Conference Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history dedicated to the 80th anniversary of the birth of Professor Michel Desa
May 16, 2019 10:40
2. Endomorphisms of graded projective modules
I. N. Balaba, A. V. Mikhalev
XV International Conference Algebra, Number Theory and Discrete Geometry: modern problems and applications, dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich
May 31, 2018 10:40

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