Nilideals of Jordan triple systems with finiteness conditions
type: Item
instance of: scholarly article
title: Nilideals of Jordan triple systems with finiteness conditions
zbMATH Open document ID: 0576.17015
DOI: 10.1007/BF00968970
author: A. V. Chekhonadskikh
published in: Siberian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The main results of this paper are as follows: 1) A quasi-regular ideal I of a Jordan triple system (Jordan pair) J which satisfies the minimal condition for inner ideals of J contained in I is nilpotent, and I is also an Artinian module over the ring of scalars. 2) A nil ideal I of a Jordan triple system (Jordan pair) J which satisfies the maximal condition for inner ideals of J contained in I is nilpotent, and I is also a Noetherian module over the ring of scalars. 3) If N is a nil subalgebra of a Jordan algebra which satisfies a chain condition on annihilators, then N is solvable.
Mathematics Subject Classification ID: 17C99
Mathematics Subject Classification ID: 17A40
zbMATH DE Number: 3920748
zbMATH Keywords: Jordan triple system
zbMATH Keywords: Jordan pair
zbMATH Keywords: nil ideal
MaRDI profile type: Publication
cites work: The Zelmanov nilpotence theorem for quadratic Jordan algebras
cites work: The Zelmanov annihilator and nilpotence of the nil radical in quadratic Jordan algebras with chain conditions
cites work: Von Neumann regularity in Jordan triple systems
cites work: Q3884273
cites work: Q3889234
full work available at URL: https://doi.org/10.1007/bf00968970
OpenAlex ID: W2075923492
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description: scientific article; zbMATH DE number 3920748