Various contributors to recent philosophy of mathematics have taken Richard Dedekind to be the founder of structuralism in mathematics. In this paper I examine whether Dedekind did, in fact, hold structuralist views and, insofar as that is the case, how they relate to the main contemporary variants. In addition, I argue that his writings contain philosophical insights that are worth reexamining...

In 1977 Hartwig and Luh asked whether an element a in a Dedekind-finite ring R satisfying aR = a2R also satisfies Ra = Ra2. In this paper, we answer this question in the negative. We also prove that if a is an element of a Dedekind-finite exchange ring R and aR = a2R, then Ra = Ra2. This gives an easier proof of Dischinger’s theorem that left strongly π-regular rings are right strongly π-regula...

Abstract Let R be an integral domain with $qf(R)=K$ , and let $F(R)$ the set of nonzero fractional ideals . Call a dually compact (DCD) if, for each $I\in F(R)$ ideal $I_{v}=(I^{-1})^{-1}$ is finite intersection principal ideals. We characterize DCDs show that class properly contains various classes domains, such as Noetherian, Mori, Krull domains. In addition, we Schreier DCD greatest common d...

Theorem 1.1. Let G be a group of Dirichlet characters modulo n, and KG the associated field. Fix a prime number p, and let H1 ⊂ H2 ⊂ G be the groups of χ such that χ(p) = 1 or χ(p) 6= 0 respectively. Then G/H2 ∼= IKG,p ⊂ Gal(KG/Q), and G/H1 ∼= DKG,p (note that these are non-canonical isomorphisms). We are now ready to prove the theorem on factoring Dedekind zeta functions of sub-cyclotomic fiel...