relation between ideals and ideals generated by sets...

Lolyta · September 30th, 2013, 01:33 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, 04:35 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, 01:33 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, 04:35 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
$Lolyta is offline$

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