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- W173739211 abstract "Publisher Summary This chapter focuses on rings and algebras. The development of ring theory has been in two directions. On one hand, such instances as the quaternions and matrix algebras gave rise to the subject of linear associative algebras, which developed into the study of Artinian and Noetherian rings. On the other hand, there are the rings of algebraic integers; they are essentially Dedekind rings, which arose also in algebraic geometry as coordinate rings of curves and which formed the beginning of a very active field of study, called the commutative ring theory, which in the last few decades has had a powerful impetus from algebraic geometry. A central part of ring theory is the classification of semi-simple rings, particularly the Wedderburn theorems. There are two main approaches. The first is via semi-simple modules, possibly using homological algebra. The other is via the Jacobson structure theory, which allows the result to be derived with a minimum of assumptions." @default.
- W173739211 created "2016-06-24" @default.
- W173739211 creator A5016875060 @default.
- W173739211 date "1977-01-01" @default.
- W173739211 modified "2023-09-26" @default.
- W173739211 title "Rings and Algebras" @default.
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- W173739211 doi "https://doi.org/10.1016/b978-0-408-70913-2.50013-9" @default.
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