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subring

Defines: 
ideal
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

20-00 no label found16-00 no label found13-00 no label found

Comments

The subset S of Z[X] which consists of polynomials with positive constant term is closed under addition and multiplication, but S is not subring of Z[X].

The sufficient (and necessary) subring criterion is that the non-empty S is closed under subtraction and multiplication.

the proper way is not to post a message but to file a correction, no point in doing both
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

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