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Semigroups and Their Subsemigroup Lattices
Preface. Part Semigroups with Certain Types of Subsemigroup Lattices. I. Preliminaries. II. Semigroups with Modular or Semimodular Subsemigroup Lattices. III. Semigroups with Complementable Subsemigroups. IV. Finiteness Conditions. V. Inverse Semigroups with Certain Types of Lattices of Inverse Subsemigroups. VI. Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups. Part Properties of Subsemigroup Lattices. VII. Lattice Characteristics of Classes of Semigroups. VIII. Embedding Lattices in Subsemigroup Lattices. Part Lattice Isomorphisms. IX. Preliminaries on Lattice Isomorphisms. X. Cancellative Semigroups. XI. Commutative Semigroups. XII. Semigroups Decomposable into Rectangular Bands. XIII. Semigroups Defined by Certain Presentations. XIV. Inverse Semigroups. Bibliography. Index. List of Notations. List of Subsections Containing Unsolved Problems or Open Questions.
396 pages, Paperback
First published October 31, 1996
About the author
L.N. Shevrin
4 booksLev Naumovich Shevrin (Russian: Лев Наумович Шеврин) - Soviet and Russian scientist mathematician and teacher, Doctor of Physics and Mathematics (1967), Professor (1969), Honorary Professor of the Ural State University (2000). Honored Scientist of the Russian Federation (1993).
Doctor of Physical and Mathematical Sciences (1967), Professor (1969), Academician of the European Academy of Sciences (2002).
Graduated from the Physics and Mathematics Faculty of the Ural University with a degree in Mathematics (1957). He has been teaching at the university since 1960. In 1968–2001. headed the Department of Algebra and Geometry (since 1995 - the Department of Algebra and Discrete Mathematics), since 2001 is the scientific director of this department. Chief Researcher of the Research Institute of Physics and Applied Mathematics of the Ural University, since 1994 he has been in charge of the laboratory of combinatorial algebra of this Research Institute organized by him (in 2005 it was transformed into a department).
At the Ural University LN Shevrin read a large number of general and special mathematical courses, supervised numerous special seminars. Developed (1979) and reads at the Faculty of Mathematics teachers at the University of the original course "Mastery of a lecturer-mathematician." Since 1996 he has been conducting a unique seminar for undergraduates and postgraduates "Stylistics of oral and written scientific speech." He lectured at other universities in Russia and foreign countries.
L. N. Shevrin is a student of Professor P. G. Kontorovich. He is a prominent scientist and teacher, one of the world's leading specialists in the theory of semigroups. LN Shevrin's research made a significant contribution to the development of a number of directions in the theory of semigroups: lattice properties, finiteness conditions, dense embeddings, structural theory of epigroups. Author of over 200 papers, including three monographs and several large review articles.
He is the founder (1966) and head of the scientific seminar "Algebraic Systems". By 2010, more than 1,100 meetings of this workshop have been held; over the years of the seminar, more than 250 mathematicians, including more than 150 people from 48 cities of the former Soviet Union and from 20 cities of 16 foreign countries, made presentations at it. Under the leadership of L. N. Shevrin, the participants of the seminar carried out several cycles of fundamental research devoted to the theory of varieties, algorithmic problems and derived structures for a number of classical types of algebraic systems: semigroups, groups, associative and Lie algebras, lattices. LN Shevrin prepared more than 30 candidates of sciences and 9 doctors of sciences, all in all, the participants of the seminar "Algebraic systems" defended more than 60 candidate and 11 doctoral dissertations. Created by L.N. Shevrin's scientific school has a high reputation in our country and has received wide international recognition. The interests of this school cover the main sections of general algebra and its applications. Research carried out in it since the beginning of the 1990s. were repeatedly supported by various grants - Russian and international. In particular, in 2003, L. N. Shevrin's school was awarded a presidential grant to support the leading scientific schools of the Russian Federation.
L.N.Shevrin was the initiator of the all-Union symposia on the theory of semigroups and the chairman of the organizing committees of all three such symposia (Sverdlovsk, 1969, 1978, 1988), was a member of the organizing committees and program committees of many other algebraic conferences, including international ones. At the Second Russian Philosophical Congress (Yekaterinburg, 1999) he was co-chairman of the section "Philosophical Foundations of Mathematics and Informatics". He was the chairman of the board of the Ural Mathematical Society (1980-2007). Member of the editorial boards of the journal
Doctor of Physical and Mathematical Sciences (1967), Professor (1969), Academician of the European Academy of Sciences (2002).
Graduated from the Physics and Mathematics Faculty of the Ural University with a degree in Mathematics (1957). He has been teaching at the university since 1960. In 1968–2001. headed the Department of Algebra and Geometry (since 1995 - the Department of Algebra and Discrete Mathematics), since 2001 is the scientific director of this department. Chief Researcher of the Research Institute of Physics and Applied Mathematics of the Ural University, since 1994 he has been in charge of the laboratory of combinatorial algebra of this Research Institute organized by him (in 2005 it was transformed into a department).
At the Ural University LN Shevrin read a large number of general and special mathematical courses, supervised numerous special seminars. Developed (1979) and reads at the Faculty of Mathematics teachers at the University of the original course "Mastery of a lecturer-mathematician." Since 1996 he has been conducting a unique seminar for undergraduates and postgraduates "Stylistics of oral and written scientific speech." He lectured at other universities in Russia and foreign countries.
L. N. Shevrin is a student of Professor P. G. Kontorovich. He is a prominent scientist and teacher, one of the world's leading specialists in the theory of semigroups. LN Shevrin's research made a significant contribution to the development of a number of directions in the theory of semigroups: lattice properties, finiteness conditions, dense embeddings, structural theory of epigroups. Author of over 200 papers, including three monographs and several large review articles.
He is the founder (1966) and head of the scientific seminar "Algebraic Systems". By 2010, more than 1,100 meetings of this workshop have been held; over the years of the seminar, more than 250 mathematicians, including more than 150 people from 48 cities of the former Soviet Union and from 20 cities of 16 foreign countries, made presentations at it. Under the leadership of L. N. Shevrin, the participants of the seminar carried out several cycles of fundamental research devoted to the theory of varieties, algorithmic problems and derived structures for a number of classical types of algebraic systems: semigroups, groups, associative and Lie algebras, lattices. LN Shevrin prepared more than 30 candidates of sciences and 9 doctors of sciences, all in all, the participants of the seminar "Algebraic systems" defended more than 60 candidate and 11 doctoral dissertations. Created by L.N. Shevrin's scientific school has a high reputation in our country and has received wide international recognition. The interests of this school cover the main sections of general algebra and its applications. Research carried out in it since the beginning of the 1990s. were repeatedly supported by various grants - Russian and international. In particular, in 2003, L. N. Shevrin's school was awarded a presidential grant to support the leading scientific schools of the Russian Federation.
L.N.Shevrin was the initiator of the all-Union symposia on the theory of semigroups and the chairman of the organizing committees of all three such symposia (Sverdlovsk, 1969, 1978, 1988), was a member of the organizing committees and program committees of many other algebraic conferences, including international ones. At the Second Russian Philosophical Congress (Yekaterinburg, 1999) he was co-chairman of the section "Philosophical Foundations of Mathematics and Informatics". He was the chairman of the board of the Ural Mathematical Society (1980-2007). Member of the editorial boards of the journal
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