Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Rings of weak dimension one and syzygetic ideals

Author: Francesc Planas-Vilanova
Journal: Proc. Amer. Math. Soc. 124 (1996), 3015-3017
MSC (1991): Primary 13F05, 13A30; Secondary 13D03
MathSciNet review: 1328371
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Abstract: We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the André-Quillen homology.

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Francesc Planas-Vilanova
Affiliation: Departament de Matemàtica Aplicada I, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, E-08028 Barcelona, Spain

Keywords: Ideal of linear type, syzygetic ideal, weak dimension, homology of commutative rings
Received by editor(s): November 4, 1994
Received by editor(s) in revised form: April 18, 1995
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society