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Encyclopedia > Simple algebra

In mathematics, an algebra is simple if it contains no non-trivial ideals. Euclid, detail from The School of Athens by Raphael. ... Algebra is the current mathematics collaboration of the week! Please help improve it to featured article standard. ... In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. ...

Simple algebras (and semi-simple algebras) were completely classified in 1907 by Joseph Wedderburn in his doctoral thesis with the title On hypercomplex numbers which appeared in the Proceedings of the London Mathematical Society. In his thesis he showed that any simple algebra is isomorphic to a matrix algebra over some division ring. This result was later generalized to semisimple rings in the Artin–Wedderburn theorem In mathematics, the term semisimple is used in a number of related ways, within different subjects. ... Joseph Henry Maclagen Wedderburn (2 February 1882- 9 October 1948) was a Scottish mathematician, who from 1909 had positions at Princeton University. ... Doctor of Philosophy (Ph. ... The London Mathematical Society (LMS) is the leading mathematical society in England. ... ... In abstract algebra, a division ring, also called a skew field, is a ring with 0 ≠ 1 and such that every non-zero element a has a multiplicative inverse (i. ... In mathematics, the term semisimple is used in a number of related ways, within different subjects. ... In abstract algebra, the Artin–Wedderburn theorem is a classification theorem for semisimple rings. ...


In mathematics, the Brauer group arose out of an attempt to classify division algebras over a given field K. It is an abelian group with elements isomorphism classes of division algebras over K, such that the center is exactly K. The group is named for the algebraist Richard Brauer. ... In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ... The term center is used in various contexts in abstract algebra to denote the set of all those elements that commute with all other elements. ...

See also

  Results from FactBites:
Simple - Wikipedia, the free encyclopedia (456 words)
In music a simple interval is one which lies within one octave, contrasted with a compound interval which exceeds or is wider than one octave.
Simple living or voluntary simplicity is an alternative lifestyle to consumerism.
Simple is an adjective to refer to the things that have a property being defined or consist of a small number, (the number of parts, or especially, the number of (different) (inter)dependencies).
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