ABSTRACT

It was Dedekind (1831–1916) who investigated the properties of the ring of integers of an algebraic number field – hence the name Dedekind domain. It is shown that every nonzero ideal of a Dedekind domain is expressible as a product of prime ideals uniquely. A brief account of integral domains having finite norm property is given. The role of fractional ideals is highlighted to show that in a Dedekind domain, every fractional ideal is invertible.