Semigroups and Automata. SELECTA Uno Kaljulaid (1941 – 1999).
Title:
Semigroups and Automata. SELECTA Uno Kaljulaid (1941 – 1999).
Author:
Peetre, J.
ISBN:
9781607501572
Personal Author:
Physical Description:
1 online resource (496 pages)
Contents:
Title page -- Contents -- Preface -- Biography of Uno Kaljulaid -- Bibliography of Uno Kaljulaid -- Representations of semigroups and algebras -- [K69a] On the cohomological dimension of some quasiprojective varieties -- [K77a] Triangular products of representations of semigroups and associative algebras -- [K79a] Triangular products and stability of representations. Candidate dissertation -- [K79b] Triangular products and stability of representations. (Author review of Candidate thesis in Physico-Mathematical Sciences) -- [K87a] Some remarks on Shevrin's problem -- [K90] Transferable elements in group rings -- [K00] Omega-rings and their flat representations -- Automata theory -- Preamble -- Automata and their decomposition -- [K97] On two algebraic constructions for automata -- [K98c] Revisiting wreath products, with applications to representations and invariants -- Majorization -- Generalized majorization -- Van der Waerden's conjecture and hyperbolicity -- On generalized majorization -- Combinatorics -- [K88a] On Stirling and Lah numbers -- Letter (or draft of letter) c. 1991 from Uno Kaljulaid to Torbjorn Tambour -- On Fibonacci numbers of graphs -- History of Mathematics -- Th. Molien, an innovator of algebra -- [K87e] On the results of Molien about invariants of finite groups and their renaissance in contemporary mathematics -- Theodor Molien, about his life and mathematical work as seen a century later. (A biographical sketch and a glimpse of his work) -- Notes on five 19th century Tartu mathematicians (Backlund, Kneser, Lindstedt, Molien, Weihrauch) -- Popularization of Mathematics -- [K68a] and [K69b] On the geometric methods of Diophantine Analysis -- [K68b] Lenin prize for work in Diophantine geometry -- [K69c] The history of solving equations -- [K70] Additional remarks on groups -- [K73a] Polynomials and formal series.
[K75a] On Galois theory -- [K75b] Theory of automata -- [K93c] Mordell's problem -- [K96] On two discrete models in connection with structures of mathematics and language -- Index of Names -- Subject Index.
Abstract:
This volume provides a selection of previously published papers and manuscripts of Uno Kaljulaid, an eminent Estonian algebraist of the last century. The central part of the book is the English translation of Kaljulaid's 1979 Candidate thesis, which originally was typewritten in Russian and manufactured in not so many copies. The thesis is devoted to representation theory in the spirit of his thesis advisor B.I. Plotkin: representations of semigroups and algebras, especially extension to this situation, and application of the notion of triangular product of representations for groups introduced by Plotkin. Through representation theory, Kaljulaid became also interested in automata theory, which at a later phase became his main area of interest. Another field of research concerns combinatorics. Besides being an outstanding and most dedicated mathematician, Uno Kaljulaid was also very much interested in the history of mathematics. In particular, he took a vivid interest in the life and work of the great 19th century Dorpat-Tartu algebraist Th. Molien. Kaljulaid was also very interested in teaching and exposition, or popularization of mathematics. Some of his more popular-scientific papers were published in an Estonian language journal Matemaatika ja Kaasaeg (Mathematics and Our Age). Among them, there is a whole series of papers about algebraic matters, culminating in a brilliant, elementary - although partly rather philosophical - essay devoted to Galois theory. Another such series is his excellent essay of Diophantine Geometry in various installments, followed by his 'éloge' to another of his teachers Yu. I. Manin. It is believed that the inclusion of these papers here will make it more interesting for beginners, and perhaps even contribute to attracting young people to mathematics.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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