Boris Novikov
(01.03.1946 – 30.03.2014)

Boris Novikov, Doctor of Sciences, professor of the Kharkiv National University, died on the 30th of March 2014. His sudden death is a great loss both to the mathematical community of Kharkiv and to the Ukrainian mathematics in general.

Boris Novikov was born on the 1st of March 1946 in Tashkomur (Kyrgyzstan) in a family of a school teacher. Soon his parents moved to Brianka (Luhansk region, Ukraine). After leaving school Boris was admitted to the Department of mechanics and mathematics of the Moscow State University. Soon he transferred to the Department of mechanics and mathematics of the Kharkiv University.

From 1969, after graduating from the university, he worked as a research fellow at the Institute of Economics of the Ukrainian Academy of Sciences. In 1972, he became a research assistant of the Department of mechanics and mathematics of the Kharkiv University. Since then, his life was continuously bound to this Department. It was here where he started his scientific research as a student of Lazar Gluskin, one of the leading experts in the theory of semigroups. Already in his first works Boris Novikov developed a quite new area, namely, the theory of 0-cohomologies, and established its relations both to the ``classical'' cohomologies and to the projective representations of semigroups. It was the core of his Ph.D. thesis which he defended in 1980. Moreover, this theory became the ground of his vast research in the cohomology theory and representations of semigroups. On this base in 1982 Novikov negatively answered the Mitchell's question whether the monoids with cancellation of cohomological dimension 1 are partially free. In this connection, he also developed the theory of partial modules over semigroups and partial cohomologies of semigroups. He also discovered the condition in order that the so defined partial cohomologies coincide with the usual ones. In 1984 Novikov gave an answer to the question formulated by P.Cohn in his famous book ``Free Rings and Their Relations''. The question was whether a monoid with cancellation without trivial units is necessarily commutative if the right and left ideals generated by any of its elements coincide. Novikov showed that it is true if the monoid has two generators, but if this number increases even to three, the answer becomes negative. Later on he proved that if a semigroup with cancellation is commutative of cohomological dimension 1, then it is either the additive group of integers or a subsemigroup of the semigroup of nonnegative integers. Finally, in 1998 he proved that a semigroup with cancellation of cohomological dimension 1 can be embedded into a free group. In 1999 he defended the Doctor of Sciences theses, based on these achievements. Soon afterwards he became Professor of the chair of functional analysis and theory of functions.

Since then he carried on an active pedagogical job. In particular, due to his efforts, the classical course of linear algebra was completely reformatted at the Kharkiv University. He also developed an essentially new course of general algebra dedicated to the group theory, as well as several special courses in the cohomology theory and the theory of semigroups. He was the head of the Kharkiv algebraic seminar, the supervisor of the Ph.D. thesis of L.Polyakova and N.Khripchenko. In his works with Khripchenko he introduced a new class of incidence algebras and started their investigation. Novikov also applied the theory of the cohomologies of semigroups to the study of Brauer monoids introduced shortly before by Svidler. He discovered that idempotents of this monoid precisely correspond to the modifications of the Galois group (the notion introduced by Novikov himself) and that the semigroup generated by such an idempotent is isomorphic to the second group of 0-cohomologies of the respective modification with the coefficients from the multiplicative group of the field. In particular, he described the modifications of cyclic groups and consequently the Brauer monoids of finite fields. The results in the cohomology theory of semigroups and its applications were the subject of the survey written by Novikov for the ``Handbook of Algebra'' series in 2008.

During the last several years Novikov, in cooperation with Dokuchaev, developed a new area of research, namely, the theory of partial actions and partial projective representations of groups. It turns out that this very special field of algebra rooting in the functional analysis is applicable to some problems of computer science. That is why Novikov moved to the chair of informatics. Here he suggested to use partial actions of free monoids for software analysis, which gave a new mathematical tool to study systems of complex event processing. In addition to the algebraic seminar, he led the seminar on the cryptography. He became an active member of the Ukrainian Federation of Informatics, where he led the Committee K-2 ``Informatics and Computer Sciences''. He received a grant allowing him to do his research at the University of Sao Paulo for half a year and went there in February 2014. But unfortunately this work only lasted one month.

Boris Novikov was a vice-editor of the journal ``Algebra and Discrete Mathematics'', a member of the editorial board of the ``Ukrainian Mathematical Bulletin'', a member of the program committee of the biannual International Algebraic Conference in Ukraine. He was the author of 54 scientific publications in Ukrainian and international mathematical journals. His works were presented at numerous scientific conferences both in Ukraine and abroad. They were highly estimated by the mathematicians working in the theory of semigroups and related topics.

Boris Novikov actively participated in the political processes exciting our country. He was one of the founders and leaders of the civil organization ``Elections-89'', a member of the Kharkiv city council, where he supervised the problems of education.

Boris Novikov was not only an outstanding mathematician, but also a brilliant, intelligent person always eager to help. He had many friends at his University, in his town, in Ukraine and abroad. We will always remember him and we extremely regret that Boris is no more with us.


V. Bondarenko, M. Chernikov, I. Chueshov,
M. Dokuchaev, Yu. Drozd, S. Favorov,
V. Gordevskiy, V. Kirichenko, M. Komarnitski,
V. Korobov, I. Kozhukhov, V. Lysytsia,
S. Ovsienko, A. Petravchuk, A. Rutkas,
V. Sushchansky, Yu. Sysak, A. Yampolskiy,
G. Zholtkevich, A. Zhuchok, Yu. Zhuchok

  Table of contents ADM - Volume 18 (2014) Number 1
    O. D. Artemovych Minimal non-PC-groups

full text in

  A. K. Asboei,
S. S. Amiri,
A. Iranmanesh
A new characterization of alternating groups full text in
  B. Bajorska,
V. Sushchansky
On a factorization of an iterated wreath product of permutation groups full text in
  E. Bondar L-cross-sections of the finite symmetric semigroup full text in
  S. Chattopadhyay,
P. Panigrahi
Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups full text in
  V. S. Gavran,
V. V. Stepukh
On weakly semisimple derivations of the polynomial ring in two variables full text in
  O. Gutik On closures in semitopological inverse semigroups with continuous inversion full text in
  A. I. Kashu Preradicals, closure operators in R-Mod and connection between them full text in
  S. Kozerenko,
V. Skochko
On graphs with graphic imbalance sequences full text in
  O. Lezama,
C. Gallego
Matrix approach to noncommutative stably free modules and Hermite rings full text in
  Yu. Movsisyan,
S. Davidov,
M. Safaryan
Construction of free g-dimonoids full text in
  B. V. Zabavsky,
B. M. Kuznitska
Effective ring full text in
  all abstracts in pdf