Solvable and nilpotent structures
type: Item
instance of: scholarly article
title: Solvable and nilpotent structures
zbMATH Open document ID: 0681.03018
author: Akito Tsuboi
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1988-01-01T00:00:00Z
review text: Summary: In Arch. Math. Logic 27, No.2, 193-197 (1988; Zbl 0661.03026), we have proven that every \(non\)-\(\aleph_ 1\)-categorical connected nilpotent group of finite Morley rank has the center Z(G) with RM(Z(G))\(\geq 2\). If a connected nilpotent group has finite Morley rank, then it is easy to see that the center is infinite. So the above result shows if G is \(non\)- \(\aleph_ 1\)-categorical the center has a rather complicated structure. The present paper is a natural continuation of the mentioned paper. Here we introduce the notion of *-nilpotency, and prove *-versions of our earlier results (see Theorems 2.3, and 2.6). Since our setting is rather general, we can apply our results to \(\omega\)-stable ring theory.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 4114602
zbMATH Keywords: categoricity
zbMATH Keywords: nilpotent group
zbMATH Keywords: finite Morley rank
zbMATH Keywords: center
zbMATH Keywords: *-nilpotency
zbMATH Keywords: \(\omega\)-stable ring theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195173931
OpenAlex ID: W2058352589
cites work: Completeness of Boolean powers of Boolean algebras
DOI: 10.2977/PRIMS/1195173931
description: scientific article; zbMATH DE number 4114602