Subring of an infinite finitley generated rng

jams · March 2nd, 2012, 08:44 AM

Show that every infinite, finitley generated ring $<R,+,.>$ has an infinite subrng $<S,+,.>$ s.t. $lt;R,+,.=>\not=<S,+,.=>=$ .

I'm not sure how to go about starting to prove this, any hits or anything would be great

Turgul · March 4th, 2012, 09:50 PM

What are subrings of the integers?

What are other infinite finitely generated rings? What are their subrings?

jams · March 5th, 2012, 01:59 PM

The subrngs of the integers would be $<n\mathbb{Z},+,.>$ for $n\in\mathbb{Z}$ as we don't need the identity in a rng

March 2nd, 2012, 08:44 AM	#1
jams Newbie Joined: Mar 2012 Posts: 3 Thanks: 0	Subring of an infinite finitley generated rng Show that every infinite, finitley generated ring $<R,+,.>$ has an infinite subrng $<S,+,.>$ s.t. $lt;R,+,.=>\not=<S,+,.=>=$ . I'm not sure how to go about starting to prove this, any hits or anything would be great
$jams is offline$

March 4th, 2012, 09:50 PM	#2
Turgul 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?
$Turgul is offline$

March 5th, 2012, 01:59 PM	#3
jams Newbie Joined: Mar 2012 Posts: 3 Thanks: 0	Re: Subring of an infinite finitley generated rng The subrngs of the integers would be $<n\mathbb{Z},+,.>$ for $n\in\mathbb{Z}$ as we don't need the identity in a rng
$jams is offline$

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Example of a subring	bWolf	Abstract Algebra	6	December 18th, 2012 12:45 PM
Prove a subring of a homomorphism	HairOnABiscuit	Abstract Algebra	2	October 2nd, 2012 05:58 PM
Prove a set is a subring of the reals	HairOnABiscuit	Abstract Algebra	11	September 11th, 2012 12:37 PM
prove that 2Z is a subring of Z	rayman	Abstract Algebra	5	February 21st, 2012 08:08 AM
subring and fields	just17b	Abstract Algebra	1	December 12th, 2007 02:57 PM