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 March 2nd, 2012, 07:44 AM #1 Newbie   Joined: Mar 2012 Posts: 3 Thanks: 0 Subring of an infinite finitley generated rng Show that every infinite, finitley generated ring $$ has an infinite subrng $$ s.t. $lt;R,+,.=>\not==$. I'm not sure how to go about starting to prove this, any hits or anything would be great
 March 4th, 2012, 08:50 PM #2 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 Re: Subring of an infinite finitley generated rng What are subrings of the integers? What are other infinite finitely generated rings? What are their subrings?
 March 5th, 2012, 12:59 PM #3 Newbie   Joined: Mar 2012 Posts: 3 Thanks: 0 Re: Subring of an infinite finitley generated rng The subrngs of the integers would be $$ for $n\in\mathbb{Z}$ as we don't need the identity in a rng

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