Omega-categorical groups and rings of finite dimension

TL;DR

This paper characterizes finite-dimensional omega-categorical groups and rings, showing they have specific structural decompositions involving finiteness, abelian properties, and null components.

Contribution

It establishes new structural theorems for finite-dimensional omega-categorical groups and rings, detailing their finite-by-abelian-by-finite and virtually finite-by-null forms.

Findings

Finite-dimensional omega-categorical groups are finite-by-abelian-by-finite.

Finite-dimensional omega-categorical rings are virtually finite-by-null.

Provides a classification framework for these algebraic structures.

Abstract

We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.