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An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series.
Amalie Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's theorem, which is fundamental in mathematical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed some theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings; rings of algebraic integers, including the ordinary integers ; and p-adic integers.
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings, as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
In mathematics, the ring of integers of an algebraic number field is the ring of all algebraic integers contained in . An algebraic integer is a root of a monic polynomial with integer coefficients: . This ring is often denoted by or . Since any integer belongs to and is an integral element of , the ring is always a subring of .
Sir Martin John Taylor, FRS is a British mathematician and academic. He was Professor of Pure Mathematics at the School of Mathematics, University of Manchester and, prior to its formation and merger, UMIST where he was appointed to a chair after moving from Trinity College, Cambridge in 1986. He was elected Warden of Merton College, Oxford on 5 November 2009, took office on 2 October 2010 and retired in September 2018.
Joachim "Jim" Lambek was a German-born Canadian mathematician. He was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
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Israel Nathan Herstein was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
Paul Moritz Cohn FRS was Astor Professor of Mathematics at University College London, 1986–1989, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.
Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Shreeram Shankar Abhyankar was an Indian American mathematician known for his contributions to algebraic geometry. He, at the time of his death, held the Marshall Distinguished Professor of Mathematics Chair at Purdue University, and was also a professor of computer science and industrial engineering. He is known for Abhyankar's conjecture of finite group theory.
James Frazier Barker is the former president of Clemson University.
Stephen Lichtenbaum is an American mathematician who is working in the fields of algebraic geometry, algebraic number theory and algebraic K-theory.
Rekha Rachel Thomas is a mathematician and operations researcher. She works as a professor of mathematics at the University of Washington, and was the Robert R. and Elaine F. Phelps Professor there from 2008 until 2012. Her research interests include mathematical optimization and computational algebra.
The Journal of Commutative Algebra is a peer-reviewed academic journal of mathematical research that specializes in commutative algebra and closely related fields. It has been published by the Rocky Mountain Mathematics Consortium (RMMC) since its establishment in 2009. It is currently published four times per year.
Jürgen Reinhard Gerhard Herzog is an Emeritus Professor of Mathematics at University of Duisburg-Essen, in Essen, Germany. From 1969 to 1975, he was Lecturer at University of Regensburg and from 1975 to 2009 a professor of Mathematics at University of Duisburg-Essen.
Jan-Erik Ingvar Roos was a Swedish mathematician.
Henry Koewing "Hal" Schenck is an American mathematician, known for his work in algebraic geometry and commutative algebra. He holds the Rosemary Kopel Brown Eminent Scholars Chair in mathematics at Auburn University.
References
- ↑ "Jim Coykendall Mathematical and Statistical Sciences". Clemson University. Retrieved 4 April 2022.
- 1 2 3 "News from around the college: leadership changes" (PDF). Ideas. Clemson University. 2013. Retrieved 4 April 2022.
- ↑ Coykendall, James Barker (1995). Normsets and rings of algebraic integers (PhD). Cornell University. ProQuest 9528210.
- ↑ {{ MathGenealogy }} template missing ID and not present in Wikidata.
- ↑ "Jim Coykendall Professor of Mathematics/James A. Meier Professor". North Dakota State University. Retrieved 4 April 2022.
- ↑ Coykendall, Jim; Schenck, Hal (2009). "Preface". 10.1216/JCA-2009-1-1-1. 1 (1): 1–2. doi:10.1216/JCA-2009-1-1-1.