The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

This talk will provide a snapshot of contemporary commutative algebra. In classical commutative algebra and algebraic number theory, the Dedekind domains are the most important class of rings. Modern commutative algebra studies numerous generalizations of the Dedekind domains in attempts to generalize results of algebraic number theory. This talk will introduce a few important generalizations o...

These notes record the basic results about DVR’s (discrete valuation rings) and Dedekind rings, with at least sketches of the non-trivial proofs, none of which are hard. This is standard material that any educated mathematician with even a mild interest in number theory should know. It has often slipped through the cracks of Chicago’s first year graduate program, but then we would need at least...