A Dedekind algebra is an ordered pair (B, h) where B is a nonempty set and h is a "similarity transformation" on B. Among the Dedekind algebras is the sequence of positive integers. Each Dedekind algebra can be decomposed into a family of disjointed, countable subalgebras which are called the configurations of the algebra. There are many isomorphic types of configurations. Each Dedekind algebra...

Abstract Dedekind type DC sums and their generalizations are defined in terms of Euler functions generalization. Recently, Ma et al. (Adv. Differ. Equ. 2021:30 2021) introduced the poly-Dedekind by replacing function appearing sums, they were shown to satisfy a reciprocity relation. In this paper, we consider two kinds new sums. One is unipoly-Dedekind sum associated with 2 unipoly-Euler expres...

Dedekind symbols generalize the classical Dedekind sums (symbols). The symbols are determined uniquely by their reciprocity laws up to an additive constant. There is a natural isomorphism between the space of Dedekind symbols with polynomial (Laurent polynomial) reciprocity laws and the space of cusp (modular) forms. In this article we introduce Hecke operators on the space of weighted Dedekind...

In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms. 2000 Mathematics subject classification: primary 20D45; secondary 16S34.

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...