relation between ideals and ideals generated by sets...

Lolyta · September 30th, 2013, 02:33 AM

Hi. I'd like to have some help in the trial of prooving the next properties for a homomorphism f: A ----> B of rings where I and J are ideals of A and B repectively.
i) I is contained in the inverse (f^-1) of the ideal generated by f(I)
ii) the ideal generated by (f^-1)(J) is contained in J

Thank you very much for any help.

Lolyta · September 30th, 2013, 05:35 AM

[quote="Lolyta"
ii) the ideal generated by (f^-1)(J) is contained in J

)[/quote]

Sorry, I meant the ideal generated by f((f^-1)(J)) is contained in J

September 30th, 2013, 02:33 AM	#1
Lolyta Newbie Joined: Sep 2013 Posts: 2 Thanks: 0	relation between ideals and ideals generated by sets... Hi. I'd like to have some help in the trial of prooving the next properties for a homomorphism f: A ----> B of rings where I and J are ideals of A and B repectively. i) I is contained in the inverse (f^-1) of the ideal generated by f(I) ii) the ideal generated by (f^-1)(J) is contained in J Thank you very much for any help.
$Lolyta is offline$

September 30th, 2013, 05:35 AM	#2
Lolyta Newbie Joined: Sep 2013 Posts: 2 Thanks: 0	Re: relation between ideals and ideals generated by sets... [quote="Lolyta" ii) the ideal generated by (f^-1)(J) is contained in J )[/quote] Sorry, I meant the ideal generated by f((f^-1)(J)) is contained in J
$Lolyta is offline$

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
Ideals	chappyform	Abstract Algebra	1	March 11th, 2013 06:05 AM
Ideals	tiger4	Abstract Algebra	1	April 21st, 2012 10:27 AM
Ideals	cknapp	Abstract Algebra	1	October 17th, 2009 10:15 PM
Ideals....	TTB3	Abstract Algebra	0	April 16th, 2009 01:39 PM
Operations on Ideals....	TTB3	Abstract Algebra	3	January 31st, 2009 05:40 AM