Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-18T00:13:10.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Localization of the Hasse-Schmidt Algebra

Published online by Cambridge University Press:  20 November 2018

William N. Traves
William N. Traves*
Affiliation:
Department of Mathematics, U.S. Naval Academy, 572C Holloway Road, Annapolis, MD 21402, USA, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The behaviour of the Hasse-Schmidt algebra of higher derivations under localization is studied using André cohomology. Elementary techniques are used to describe the Hasse-Schmidt derivations on certain monomial rings in the nonmodular case. The localization conjecture is then verified for all monomial rings.

Keywords

13D0313N10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 2 , 01 June 2003 , pp. 304 - 309
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] André, M., Homologie des algèbres commutatives. Springer-Verlag, Berlin, 1974.Google Scholar
[2] Brown, W. C. and Kuan, W., Ideals and higher derivations in commutative rings. Canad. J. Math. 24 (1972), 400–415.Google Scholar
[3] Brumatti, P. and Simis, A., The module of derivations of a Stanley-Reisner ring. Proc. Amer.Math. Soc. 123 (1995), 1309–1318.Google Scholar
[4] Grothendieck, A. and Dieudonné, J., Éléments de géometrie algébrique IV. Inst. Hautes É tudes Sci. Publ. Math. 32, Le Bois-Marie Bures-sur-Yvette, 1967.Google Scholar
[5] Matsumura, H., Integrable Derivations. Nagoya Math J. 87 (1982), 227–245.Google Scholar
[6] Smith, L., Polynomial invariants of finite groups. Research Notes in Mathematics 6, A. K. Peters, Ltd., Wellesley, MA, 1995.Google Scholar
[7] Traves, W. N., Differential Operators and Nakai's Conjecture. Ph.D. thesis, University of Toronto, 1998.Google Scholar
[8] Traves, W. N., Differential Simplicity and Tight Closure. J. Algebra. 228 (2000), 457–476.Google Scholar
[9] Wood, R. M. W., Problems in the Steenrod Algebra. Bull. LondonMath. Soc. (5) 30 (1998), 449–517.Google Scholar