Tensor, symmetric and exterior algebras Kähler modules

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

1. Eisenbud D., Commutative Algebra with a View Toward Algbraic Geometry, Springer Verlag, New York (1995).
2. Erdogan,A., Differential Operators and Their Universal Modules, Phd. Thesis, University of Leeds,(1993).
3. George M.Bergman, Tensor algebras, exterior algebras and symmetric algebras, http://math.berkeley.edu/ gbergman, (1997).
4. Johnson J. Kähler Differential and differential algebra, The Annals of Mathematics, Second series, Vol.89, No 1, 92–98,(1969).
5. McConnell, J.C. and Rabson, J.C. , Noncommutative Noetherian Rings, Wiley-Interscience,(1987).
6. Nakai, Y., High Order Derevations, Osaka J. Math.7,1–27,(1970).
7. Olgun, N., The Universal Differential Modules of Finitely Generated Algebras, Ph.D Thesis, Hacettepe University, (2005).
8. Olgun, N. and Erdogan, A. , Some Results On Universal Modules, Int. Mat. For. 1(15), 707-712, (2006).

9. Osborn, H., Modules of Differentials I, Math. Ann.170, 221-244, (1967).
10. Sweedler, M.E., Groups of Simple Algebras, Publ. Math. No:44. (1975).
11. Sweedler ,M.E. and Heyneman, R.G.,Affine Hopf Algebras, J.algebra 13,192–241,(1969).
12. Bourbaki, N., Elements of Mathematics, Algebra I.Chapters1–3, Springer-Verlag, (1989).
13. Mac Lane, S. and Birkhoff, G., Algebra, AMS Chelsea, (1999).