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.
Biography
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:
Balaba I. N., “O slabo primitivnykh graduirovannykh koltsakh”, UMN, 56:6 (2001), 139–140
Balaba I. N., “Ekvivalentnosti Mority kategorii graduirovannykh modulei”, UMN, 42:3 (1987), 177–178
Balaba I. N., “Refleksivnye graduirovannye moduli”, Sb.: Algoritmicheskie problemy teorii grupp i polugrupp, Tula, 1991, 88–96
Balaba I. N., “Koltsa chastnykh polupervichnykh graduirovannykh kolets”, Sb. trudov mezhdunarodnoi konferentsii «Universalnaya algebra i ee prilozheniya», Volgograd, 2000, 21–28
M. N. Dobrovol'skii, N. N. Dobrovol'skii, A. V. Afonina, N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, “Universality and antiuniversality theorems for zeta functions of monoids of natural numbers”, Chebyshevskii Sb., 24:4 (2023), 104–136
2021
2.
I. N. Balaba, A. V. Mikhalev, “Graded quasi-Frobenius rings and modules”, Intelligent systems. Theory and applications, 25:4 (2021), 66–70
2019
3.
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
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
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
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
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, no. 2, 27–39
I. N. Balaba, E. N. Krasnova, “Semisimple graded rings”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(2) (2013), 23–28
2012
9.
I. N. Balaba, A. L. Kanunnikov, A. V. Mikhalev, “Quotient rings of graded associative rings. I”, Fundam. Prikl. Mat., 17:2 (2012), 3–74; J. Math. Sci., 186:4 (2012), 531–577
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
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; J. Math. Sci., 164:2 (2010), 168–177
I. N. Balaba, “Prime graded modules”, Fundam. Prikl. Mat., 14:4 (2008), 65–74; J. Math. Sci., 163:5 (2009), 487–492
15.
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; Russian Math. Surveys, 63:3 (2008), 551–553
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; J. Math. Sci., 156:2 (2009), 209–218
I. N. Balaba, “Isomorphisms of graded endomorphism rings of progenerators”, Fundam. Prikl. Mat., 13:1 (2007), 3–10; J. Math. Sci., 152:4 (2008), 451–455
A. V. Mikhalev, I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of graded $\Omega$-groups”, Fundam. Prikl. Mat., 12:2 (2006), 159–174; J. Math. Sci., 149:2 (2008), 1146–1156
I. N. Balaba, S. A. Pikhtilkov, “Prime radicals of special Lie superalgebras”, Fundam. Prikl. Mat., 9:1 (2003), 51–60; J. Math. Sci., 128:6 (2005), 3365–3371
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; J. Math. Sci., 128:6 (2005), 3350–3364
I. N. Balaba, “Calculation of the dimension polynomial of a prime principal difference ideal”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 2, 16–20
1984
26.
I. N. Balaba, “Dimensional polynomials of extension of difference fields”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1984, no. 2, 31–35
2022
27.
I. N. Balaba, S. S. Demidov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. A. Ivanov-Pogodaev, A. Ya. Kanel-Belov, Yu. V. Nesterenko, I. Yu. Rebrova, A. L. Semenov, A. A. Fomin, V. G. Chirskii, V. N. Chubarikov, “To memory of Alexander Vasilyevich Mikhalev”, Chebyshevskii Sb., 23:5 (2022), 348–350
2021
28.
V. N. Chubarikov, A. V. Mikhalev, I. B. Kozhukhov, A. Ya. Kanel-Belov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, I. N. Balaba, A. P. Boshchenko, P. B. Zhdanovich, A. V. Kartashova, A. L. Rasstrigin, V. L. Usol'tsev, N. A. Shchuchkin, S. V. Syrovatskaya, “In memory of Vladimir Konstantinovich Kartashov”, Chebyshevskii Sb., 22:5 (2021), 419–421
29.
A. I. Shafarevich, V. N. Chubarikov, D. O. Orlov, A. O. Ivanov, A. V. Mikhalev, V. G. Chirskii, A. Yu. Ol'shanskii, M. V. Zaicev, I. B. Kozhukhov, A. Ya. Kanel-Belov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, I. N. Balaba, “In memory of Vyacheslav Alexandrovich Artamonov”, Chebyshevskii Sb., 22:5 (2021), 417–418
30.
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
31.
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
2020
32.
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; J. Math. Sci., 262:5 (2022), 592–602
2016
33.
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
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
3.
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