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4 Cards in this Set
- Front
- Back
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Ring Definitions and Axioms |
A set R and two operations +,× For every a, b, c in R a+(b+c)=(a+b)+c There exists a 0 in R a+0=a For every a there exists an a bar a+a bar = 0 For every a,b,c (a×b)×c=a×(b×c) For every a,b,c a×(b+c)=a×b+a×c (b+c)×a=b×a+c×a |
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Ring with unity |
[R,+] is an abelian group R has a multiplicative identity [R,+,×] is a ring and there exist a 1 does not equal zero in R, for every a in R 1×a=a×1=a |
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Commutative Rings |
(R,+,×) is a ring For every a,b in R a×b=b×a |
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Commutative Rings with Unity |
(R,+,×) is a ring For every a,b in R a×b=b×a There exists a 1 does not = 0 for every a 1×a=a |
