Timeline for Is there much difference between Kronecker's and Dedekind's methods in algebraic number theory and commutative algebra?
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| Jan 3, 2012 at 6:52 | comment | added | Bill Dubuque | @KConrad An English summary of Lucius' thesis is Rings with a theory of greatest common divisors, Manuscripta Math. 95, 117-136 (1998). This is the best English introduction as far as I know. | |
| Jun 1, 2010 at 19:09 | comment | added | KConrad | Yes, the "rings with a theory of divisors" in Borevich and Shafarevich are precisely Krull rings if you allow fields to have a theory of divisors with an empty set of discrete valuations (or not, if you don't consider fields to be Krull rings). An English language reference that I used to convince myself the B&S's rings are the same as Krull rings is Matsumura's Commutative Ring theory. In the list of 3 axioms for rings with a theory of divisors in B&S, on p. 171, axioms 1 and 3 imply axiom 2. My reference on that is L. Skula, "Divisorentheorie einer Halbgruppe" Math Z. 114 (1970), 113--120. | |
| Jun 1, 2010 at 13:54 | history | answered | Franz Lemmermeyer | CC BY-SA 2.5 |