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commutative ring (Definition)

Let $ (X,+,*)$ be a ring. Since $ (X,+)$ is required to be an abelian group, the operation $ +$ necessarily is commutative. This needs not to happen for $ *$. Rings where $ *$ is commutative, that is, $ x*y=y*x$ for all $ x,y\in R$, are called commutative rings.



"commutative ring" is owned by drini. [ full author list (3) | owner history (2) ]
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See Also: group of units, examples of rings


Attachments:
arithmetical ring (Theorem) by PrimeFan
polynomial function (Definition) by pahio
Marot ring (Definition) by Mravinci
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Cross-references: commutative, operation, abelian group, ring
There are 153 references to this entry.

This is version 3 of commutative ring, born on 2003-10-15, modified 2005-02-26.
Object id is 5169, canonical name is CommutativeRing.
Accessed 14682 times total.

Classification:
AMS MSC: 13A99 (Commutative rings and algebras :: General commutative ring theory :: Miscellaneous)
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