Re: Algebra with quotient ring.

On Jul 8, 11:55 am, Bill Dubuque <w...@xxxxxxxxxxxxxxxxxxxx> wrote:
mina_world <mina_wo...@xxxxxxxxxxx> wrote:

A commutative ring A is called a principal ideal ring
if every ideal of A is principal.

Show that a quotient ring of a principal ideal ring
is principal ideal ring.

In fact, I want to know that Z_n is principal ideal ring.
so, If I can show above problem, this is trivial by Z/(nZ).
But... I can't. so, I need your advice.

See my prior posthttp://google.com/groups?selm=y8z8yfyyhsn.fsf%40nestle..csail.mit.edu

--Bill Dubuque

*********************************************************8

Once again, Bill, you mislead with your (in)famous "see my prior post"
thing: the link you gave talks about localizations, not quotient
rings...*sigh*.

This misleads and confuses sombody wanting something pretty basic and
elementary, not to mention unbased claims like "The fraction ring
construction D S^-1 with denominator submonoid S < D*
preserves many properties of domains D, e.g. Euclidean, PID, UFD,
valuation, Bezout, GCD, Dedekind, Prufer, Krull, Noetherian,
integrally closed, etc."...no proofs, no links...and that "etc." one
might really be frightening to someone asking such an easy bquestion
as the OP.

A pitry, really...

Regards
Tonio
.

Relevant Pages

  • Re: Algebra with quotient ring.
    ... A commutative ring A is called a principal ideal ring ... Your prior post discusses localization, ... is about passage to the quotient. ...
    (sci.math)
  • Re: Algebra with quotient ring.
    ... Your prior post discusses localization, ... quotient. ... whenever this happens and R is principal ideal ring, ...
    (sci.math)
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