This is a glossary of commutative algebra. See also list of algebraic geometry topics,

glossary of classical algebraic geometry The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and late ...

glossary of algebraic geometry This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry. ...

glossary of ring theory Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. For the items in commutative algebra (the theor ...

and

glossary of module theory Module theory is the branch of mathematics in which module (mathematics), modules are studied. This is a glossary of some terms of the subject. See also: ''Glossary of linear algebra'', ''Glossary of ring theory'', ''Glossary of representation the ...

. In this article, all rings are assumed to be

commutative In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a pr ...

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Commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...

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