Chain conditions satisfied by some algebraic structures including ideals in certain commutative rings From http://en.wikipedia.org/wiki/Ascending_chain_condition:
"In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly, ideals in certain commutative rings.[1][2][3]
Notes
1 ^ Hazewinkel, Gubareni & Kirichenko (2004), p.6, Prop. 1.1.4.
2 ^ Fraleigh & Katz (1967), p. 366, Lemma 7.1
3 ^ Jacobson (2009), p. 142 and 147

References
    Atiyah, M. F., and I. G. MacDonald, Introduction to Commutative
    Algebra, Perseus Books, 1969, ISBN 0-201-00361-9
        Michiel Hazewinkel, Nadiya Gubareni, V. V. Kirichenko. Algebras, rings and modules. Kluwer Academic Publishers, 2004. 
    ISBN 1-4020-2690-0

        John B. Fraleigh, Victor J. Katz. A first course in abstract algebra. Addison-Wesley Publishing Company. 5 ed., 1967. 
    ISBN 0-201-53467-3

        Nathan Jacobson. Basic Algebra I. Dover, 2009. ISBN 978-0-486-47189-1"

I have the 7th edition of Fraleigh and Katz but can't find the equivalent reference.  I'm nearly sure that in another Wikipedia page it spells out what kind of ideals and commutative (semi?)rings but I can't find it any more (tab deleted somehow and can't get it back).  It also spells out why this is true.  Can anyone please point me to any references?
Thanks very much.  (Sorry about the references to Wikipedia pages.)

For example, you can check these notes.
