$\omega$-stability and Morley rank of bilinear maps, rings and nilpotent groups

TL;DR

This paper investigates the algebraic properties of ω-stable bilinear maps, rings, and nilpotent groups, providing comprehensive structure theorems especially in the finite Morley rank case.

Contribution

It offers new structure theorems for ω-stable algebraic structures and extends understanding of their properties in the finite Morley rank setting.

Findings

Complete structure theorems for ω-stable bilinear maps, rings, and nilpotent groups.

Characterization of these structures in the finite Morley rank case.

Enhanced understanding of algebraic stability and Morley rank relations.

Abstract

In this paper we study the algebraic structure of $\omega$-stable bilinear maps, arbitrary rings and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.