Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-96-03416-8
MathSciNet review: 1328371
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [A] M. André: Homologie des algèbres commutatives. Grundlehren 206. Heidelberg: Springer 1974. MR 50:4707
  • [BR] J. Barja, A. G. Rodicio: Syzygetic Ideals, Regular sequences and a Question of Simis. J. Algebra 121 (1989), 310-314. MR 90b:13017
  • [B] N. Bourbaki: Algèbre. Chapitre 10. Algèbre homologique. Masson. Paris, 1980. MR 82j:18022
  • [C] D. Costa: On the Torsion-Freeness of the Symmetric Powers of an Ideal. J. Algebra 80 (1983), 152-158. MR 85e:13019
  • [MR] A. Micali, N. Roby: Algèbres symétriques et syzygies. J. Algebra 17 (1971), 460-469. MR 44:198
  • [P] F. Planas Vilanova: Ideals de tipus lineal i homologia d'André-Quillen. Ph.D. Thesis. Universitat de Barcelona, 1994.
  • [R] J. Rotman: An Introduction to Homological Algebra. Academic Press, 1979. MR 80k:18011
  • [V] W. V. Vasconcelos: Arithmetic of Blowup Algebras. LMS Lecture Note Series 195. Cambridge University Press, 1994. MR 95g:13005

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13F05, 13A30, 13D03

Retrieve articles in all journals with MSC (1991): 13F05, 13A30, 13D03


Additional Information

Francesc Planas-Vilanova
Affiliation: Departament de Matemàtica Aplicada I, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, E-08028 Barcelona, Spain
Email: planas@ma1.upc.es

DOI: https://doi.org/10.1090/S0002-9939-96-03416-8
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

American Mathematical Society