Anton Kazimirovich Sushkevich (Антон Казимирович Сушкевич) (23 January 1889,

Borisoglebsk Borisoglebsk () is a town in Voronezh Oblast, Russia, located on the left bank of the Vorona River near its confluence with the Khopyor. Population: 65,000 (1969). History Borisoglebsk was founded in 1646 and was named for the Russian s ...

, Russia — 30 August 1961,

Kharkiv Kharkiv, also known as Kharkov, is the second-largest List of cities in Ukraine, city in Ukraine.

, Ukraine) was a Russian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...

author who expanded

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

to include

semigroup In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily th ...

s and other

magma Magma () is the molten or semi-molten natural material from which all igneous rocks are formed. Magma (sometimes colloquially but incorrectly referred to as ''lava'') is found beneath the surface of the Earth, and evidence of magmatism has also ...

s. Sushkevich attended secondary school in

Voronezh Voronezh ( ; , ) is a city and the administrative centre of Voronezh Oblast in southwestern Russia straddling the Voronezh River, located from where it flows into the Don River. The city sits on the Southeastern Railway, which connects wes ...

and studied in Berlin from 1906 to 1911. There he attended lectures of F. G. Frobenius,

Issai Schur Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the Humboldt University of Berlin, University of Berlin. He obtained his doctorate in 1901, became lecturer i ...

, and

Hermann Schwarz Karl Hermann Amandus Schwarz (; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis. Life Schwarz was born in Hermsdorf, Silesia (now Sobieszów, Poland). In 1868 he married Marie Kummer ...

. Sushkevich studied

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

with L. V. Rostropovich, father of

Mstislav Rostropovich Mstislav Leopoldovich Rostropovich (27 March 192727 April 2007) was a Russian Cello, cellist and conducting, conductor. In addition to his interpretations and technique, he was well known for both inspiring and commissioning new works, which enl ...

. In 1906 he was a

cello The violoncello ( , ), commonly abbreviated as cello ( ), is a middle pitched bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned i ...

student at

Stern Conservatory The Stern Conservatory (''Stern'sches Konservatorium'') was a private music school in Berlin with many distinguished tutors and alumni. The school is now part of Berlin University of the Arts. History It was founded in 1850 as the ''Berliner Mu ...

(now part of

Berlin University of the Arts The Universität der Künste Berlin (UdK; also known in English as the Berlin University of the Arts), situated in Berlin, Germany, is the second largest art school in Europe. It is a public art and design school, and one of the four research uni ...

). In 1911 he moved to

Saint Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

, graduating from the Imperial University in 1913. Moving to

Kharkiv Kharkiv, also known as Kharkov, is the second-largest List of cities in Ukraine, city in Ukraine.

, Suskevich taught in secondary education while he pursued a graduate degree at Kharkov State University. His dissertation was ''The theory of operations as the general theory of groups''. Obtaining the degree, he became an assistant professor at the university in 1918, and adjunct professor in 1920.

Voronezh State University Voronezh State University (, ВГУ; VSU) is one of the main universities in Central Russia, located in the city of Voronezh. The university was established in 1918 by professors evacuated from the University of Tartu in Estonia. The university ...

employed Sushkevich in 1921 as professor of mathematics. He published the first edition of his ''Higher Algebra'' (1923). He published a generalization of

Cayley's theorem In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group is isomorphic to a subgroup of a symmetric group. More specifically, is isomorphic to a subgroup of the symmetric gro ...

for certain finite semigroups in 1926. The next year he was in Moscow for the Russian Mathematical Congress, and the following year in Bologna for the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

. In Kharkiv, the Ukrainian Scientific Research Institute of Mathematics and Mechanics was established in 1929 with Sushkevich as a member. With a rising interest in

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

, he wrote a second book on algebra: ''Foundations of Higher Algebra'' which was published both in Russian and Ukrainian. In 1933 he directed the Algebra & Number Theory section of Kharkov State University's department of mathematics. At that time Stalin caused a

famine A famine is a widespread scarcity of food caused by several possible factors, including, but not limited to war, natural disasters, crop failure, widespread poverty, an Financial crisis, economic catastrophe or government policies. This phenom ...

in Ukraine, the

Holodomor The Holodomor, also known as the Ukrainian Famine, was a mass famine in Ukrainian Soviet Socialist Republic, Soviet Ukraine from 1932 to 1933 that killed millions of Ukrainians. The Holodomor was part of the wider Soviet famine of 1930–193 ...

, killing millions especially in rural areas. Suskevich survived to edit new editions of his textbook that included "new algebra":

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

integral domain In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibilit ...

ring (The) Ring(s) may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell Arts, entertainment, and media Film and TV * ''The Ring'' (franchise), a ...

ideal Ideal may refer to: Philosophy * Ideal (ethics), values that one actively pursues as goals * Platonic ideal, a philosophical idea of trueness of form, associated with Plato Mathematics * Ideal (ring theory), special subsets of a ring considered ...

s, and

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...

s. His original work, ''The Theory of Generalized Groups'' (1937) opened up the area of

s. According to biographer Hollings, "He sought to describe his semigroups of interest in terms of certain of their subgroups: from Sushkevich's point of view,

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

s were objects of known structure."Christopher Hollings (2014) ''Mathematics Across the Iron Curtain: A History of the Algebraic Theory of Semigroups'', chapter 3: Anton Kazimirovich Sushkevich, pages 45 to 76,

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Selected works

* 1928: . * 1929: "On a generalization of the associative law",

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of pure and applied mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must ...

31(1):204–14 * 1951: "Materials for the History of Algebra in Russia in the 19th and beginning of the 20th centuries", * 1954: ''Theory of Numbers'', second edition 1956

References

* Christopher Hollings (2009) "The early development of the algebraic theory of semigroups",

Archive for History of Exact Sciences ''Archive for History of Exact Sciences'' is a peer-reviewed academic journal currently published bimonthly by Springer Science+Business Media, covering the history of mathematics and of astronomy observations and techniques, epistemology of scien ...

63(5): 497–536, especially 511–513. * * Christopher Holling
Summary of "Finite groups without unique invertibiility"
(PDF) via

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{{DEFAULTSORT:Sushkevich, Anton 20th-century Russian mathematicians Russian textbook writers Algebraists Soviet textbook writers Soviet male writers Soviet mathematicians 20th-century Russian male writers