Related papers: Six Ukrainian articles on semigroup theory by A. K…
This text was written 20 years ago, inspired by M. Somekawa's paper on K-groups attached to semi-abelian varieties (K-Theory 4 (1990), 105--119) and before Voevodsky's theory of presheaves with transfers. The reason why it only had a…
We give an introduction to the ideas behind G. S. Tseytin's 1958 construction of a seven-relation semigroup with undecidable word problem. We give a history of the ideas leading up to its construction, some intuition for the proof, and…
This is an English translation of the thesis written by G. S. Makanin for the degree of Candidate of Physical and Mathematical Sciences (equivalent to a Ph.D.), originally submitted to the Steklov Mathematical Institute in 1966. The…
This is an overview of the basics of inverse semigroup theory written for the Workshop on Semigroups and Categories held at the University of Ottawa in 2010.
This paper was written as a tribute to Mario Petrich, a major figure in the history of semigroup theory. Publication is posthumous in view of his recent death.
This is an English translation of four remarkable articles, originally written in Russian, by Sergei Ivanovich Adian (1931--2020), supplemented by the translation of two closely related articles by Andrei Andreevich Markov Jr (1903--1979).…
The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…
Assume that $S$ is a semigroup generated by $\{x_1,...,x_n\}$, and let $\Uscr$ be the multiplicative free commutative semigroup generated by $\{u_1,...,u_n\}$. We say that $S$ is of \emph{$I$-typ}e if there is a bijection $v:\Uscr\r S$ such…
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
The following is an exposition of a course of algebra that Prof. Aleksandr Aleksandrovich Zykov (1922-2013) distributed among the participants of his seminar in graph theory not far away from Odessa, Ukraine, on September, 1991. It is a…
In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…
This is an expanded version of my talk given at the International Conference ``Algebra and Number Theory'' dedicated to the 80th anniversary of V. E. Voskresenskii, which was held at the Samara State University in May 2007. The goal is to…
One of the features of modern science is the formation of stable large collaborations of researchers working together within the projects that require the concentration of huge financial and human resources. Results of such common work are…
The concept of a k-translatable groupoid is introduced. Those k-translatable quadratical quasigroups induced by the additive group of integers modulo m, where k<40, are listed for m<1200. The fine structure of quadratical quasigroups is…
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
The paper presents the results of the study of international and national cooperation of Ukrainian scientists from different scientific fields using citation analysis data from Scopus in the period of 2011-2015. The results show that during…
To facilitate teaching of quantum mechanics on undergraduate and even advanced secondary school levels, we present an unabridged translation of the original German text of the famous Werner Heisenberg's breakthrough paper of 1925 into Czech…
A translation from Russian of the famous paper by Mark Krein "On the theory of symmetric polynomials" published in Math. Sb., vol. 40, no. 3, 1933, pp. 271-283.
A general equivariant shape theory for arbitrary $G$-spaces in the case of a compact group $G$ is constructed by using the method of pseudometrics suggested by Yu. M. Smirnov as early as in 1985 at the fifth Tiraspol symposium on general…