# subring

## Primary tabs

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

## Mathematics Subject Classification

### Subring criterion

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.

### Re: Subring criterion

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