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Generating Adjoint Groups

Part of: Radicals and radical properties of rings

Published online by Cambridge University Press:  30 January 2019

Be'eri Greenfeld
Be'eri Greenfeld*
Affiliation:
Department of Mathematics, Bar Ilan University, Ramat Gan, 5290002, Israel (beeri.greenfeld@gmail.com)
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Abstract

We prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated. We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated and, on the other hand, construct a finitely generated, infinite-dimensional nil algebra whose adjoint group is generated by elements of bounded torsion.

Keywords

nil ringsJacobson radicalGolod–Shafarevich algebrasadjoint grouptorsion groupsboundedly generated groupsbraces

MSC classification

Primary: 16N20: Jacobson radical, quasimultiplication
Secondary: 16N40: Nil and nilpotent radicals, sets, ideals, rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 733 - 738
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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