Tensor, symmetric and exterior algebras Kähler modules

Year 2016, Volume: 4 Issue: 3, 290 - 295, 30.09.2016

Necati Olgun Mehmet Sahin Vakkas Ulucay

Abstract

Let  be an algebraically closed field of
characteristic zero,  an affine k-algebra and let  denote its universal finite Kähler
module of differentials over . In this paper, we consider the tensor, exterior and symmetric algebras
of Kähler modules introduced by H. Osborn [9]. We explore some interesting
properties of the algebras of Kähler modules, which have not been considered
before.

Keywords

Kähler module, projective module, regular ring, tensor

References

• Eisenbud D., Commutative Algebra with a View Toward Algbraic Geometry, Springer Verlag, New York (1995).
• Erdogan,A., Differential Operators and Their Universal Modules, Phd. Thesis, University of Leeds,(1993).
• George M.Bergman, Tensor algebras, exterior algebras and symmetric algebras, http://math.berkeley.edu/ gbergman, (1997).
• Johnson J. Kähler Differential and differential algebra, The Annals of Mathematics, Second series, Vol.89, No 1, 92–98,(1969).
• McConnell, J.C. and Rabson, J.C. , Noncommutative Noetherian Rings, Wiley-Interscience,(1987).
• Nakai, Y., High Order Derevations, Osaka J. Math.7,1–27,(1970).
• Olgun, N., The Universal Differential Modules of Finitely Generated Algebras, Ph.D Thesis, Hacettepe University, (2005).
• Olgun, N. and Erdogan, A. , Some Results On Universal Modules, Int. Mat. For. 1(15), 707-712, (2006).
• Osborn, H., Modules of Differentials I, Math. Ann.170, 221-244, (1967).
• Sweedler, M.E., Groups of Simple Algebras, Publ. Math. No:44. (1975).
• Sweedler ,M.E. and Heyneman, R.G.,Affine Hopf Algebras, J.algebra 13,192–241,(1969).
• Bourbaki, N., Elements of Mathematics, Algebra I.Chapters1–3, Springer-Verlag, (1989).
• Mac Lane, S. and Birkhoff, G., Algebra, AMS Chelsea, (1999).