Boris Moiseyevich Schein (22 June 1938 – 4 October 2023) was a Russian-American mathematician, an expert in

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 a Distinguished Professor in the Department of Mathematical Sciences at the

University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a Public university, public Land-grant university, land-grant research university in Fayetteville, Arkansas, United States. It is the Flagship campus, flagship campus of the University of Arkan ...

Biography

Schein was born in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

on 22 June 1938, and moved to

Saratov Saratov ( , ; , ) is the largest types of inhabited localities in Russia, city and administrative center of Saratov Oblast, Russia, and a major port on the Volga River. Saratov had a population of 901,361, making it the List of cities and tow ...

during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. He became interested in mathematics as a teenager, and came under the influence of Viktor Wagner, a professor of mathematics at

Saratov State University Saratov Chernyshevsky State University (, СГУ, transcribed as SGU) is a higher education and research institution in Russia. In 2023 it was ranked #1,156 in the world by ''US News & World Report''. Named for Nikolay Chernyshevsky, the univer ...

. Schein did his undergraduate studies in Mechanics-Mathematics at Saratov State, and chose to specialize in

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, Wagner's subject. In 1958 he solved the problem of characterizing the

s that could be embedded into an

inverse semigroup In group (mathematics), group theory, an inverse semigroup (occasionally called an inversion semigroup) ''S'' is a semigroup in which every element ''x'' in ''S'' has a unique ''inverse'' ''y'' in ''S'' in the sense that and , i.e. a regular semigr ...

. He graduated summa cum laude in 1960. He continued working as a graduate student with Wagner, and in 1962 defended a candidacy dissertation on semigroups of transformations at the Herzen State Pedagogical University of Russia in

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 ...

. He accepted a faculty position at Saratov in 1963, and defended his

Doctor of Sciences A Doctor of Sciences, abbreviated д-р наук or д. н.; ; ; ; is a higher doctoral degree in the Russian Empire, Soviet Union and many Commonwealth of Independent States countries. One of the prerequisites of receiving a Doctor of Sciences ...

thesis in 1966, again at Herzen State Pedagogical University. In 1968, Schein was one of the founding editors of the journal '' Semigroup Forum'', published by

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

. However, in the 1970s his connections with Western mathematicians led to political difficulties, his correspondence with mathematicians outside the USSR was cut off, and his students were prevented from graduating. Eventually, in the late 1970s, his mentor Wagner retired from the university and Schein was dismissed. In 1979, Schein was able to travel to Austria with his wife and daughter, and immediately he obtained a temporary visiting position at

Tulane University The Tulane University of Louisiana (commonly referred to as Tulane University) is a private research university in New Orleans, Louisiana, United States. Founded as the Medical College of Louisiana in 1834 by a cohort of medical doctors, it b ...

New Orleans New Orleans (commonly known as NOLA or The Big Easy among other nicknames) is a Consolidated city-county, consolidated city-parish located along the Mississippi River in the U.S. state of Louisiana. With a population of 383,997 at the 2020 ...

. In 1980, he took a position at the University of Arkansas. Boris Schein is known for the Schein index, which is the least number of "concepts" necessary to express the

logical matrix A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in ...

of a

binary relation In mathematics, a binary relation associates some elements of one Set (mathematics), set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs ...

as a Boolean sum, and where a concept is an

outer product In linear algebra, the outer product of two coordinate vectors is the matrix whose entries are all products of an element in the first vector with an element in the second vector. If the two coordinate vectors have dimensions ''n'' and ''m'', the ...

of logical vectors. In 2011, Schein was named a distinguished reviewer of

Zentralblatt MATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

by the

European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The curren ...

.Professor Named Distinguished Reviewer
, Univ. of Arkansas Dept. of Mathematical Sciences, retrieved 3 February 2012. Boris M. Schein died on 4 October 2023, at the age of 85.

References

{{DEFAULTSORT:Schein, Boris M. 1938 births 2023 deaths 20th-century American mathematicians 21st-century American mathematicians Soviet mathematicians University of Arkansas faculty Scientists from Saratov Tulane University faculty Soviet emigrants to the United States American people of Russian descent Herzen University alumni