Commutative Rings and Algebras
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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to ring theory. Commutative rings are sets like the set of integers, allowing addition and (commutative) multiplication. Of particular interest are several classes of rings of interest in number theory, field theory, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. (See also Associative rings and algebras.)|
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