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Noncommutative Rings

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Algebra II

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 18))

Abstract

The algebra of square matrices of size n 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative algebra1. Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathematics. Historically however, the study of matrix algebras was preceded by the discovery of quaternions which, introduced in 1843 by Hamilton, found applications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The algebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology.

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  1. L. A. Bokhut’
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  2. I. V. L’vov
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  3. V. K. Kharchenko
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  1. Steklov Mathematical Institute, ul. Vavilova 42, 117966, Moscow, USSR

    A. I. Kostrikin  & I. R. Shafarevich  & 

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Bokhut’, L.A., L’vov, I.V., Kharchenko, V.K. (1991). Noncommutative Rings. In: Kostrikin, A.I., Shafarevich, I.R. (eds) Algebra II. Encyclopaedia of Mathematical Sciences, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72899-0_1

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