## Commutative Algebra

Let denote an -algebra, so that is a Vector Space over and

Now define

where . An Associative -algebra is commutative if for all . Similarly, a Ring is commutative if the Multiplication operation is commutative, and a Lie Algebra is commutative if the Commutator is 0 for every and in the Lie Algebra.

References

Cox, D.; Little, J.; and O'Shea, D. Ideals, Varieties, and Algorithms: An Introduction to Algebraic Geometry and Commutative Algebra, 2nd ed. New York: Springer-Verlag, 1996.

Finch, S. Zero Structures in Real Algebras.'' http://www.mathsoft.com/asolve/zerodiv/zerodiv.html.

MacDonald, I. G. and Atiyah, M. F. Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969.

Samuel, P. and Zariski, O. Commutative Algebra, Vol. 2. New York: Springer-Verlag, 1997.