He does assume they have already seen some non-archimedean fields, usually the p-adic numbers and hopefully the complete algebraically closed
p-adic field Cp, but he reviews them briefly just in case.
In the following, we assume that all algebras are over an algebraically closed
field F with characteristic zero, Id is the identity mapping, and Z is the set of integers.
We work over an algebraically closed
field of arbitrary characteristic throughout this paper.
Throughout H is a d-dimensional semisimple Hopf algebra over an algebraically closed
field k of characteristic 0 and H* is its dual which is a semisimple Hopf algebra as well.
Throughout this paper, k is an algebraically closed
field, A is a finite dimensional k-algebra.
of Newfoundland, Canada) introduce theory of gradings on Lie algebras, with a focus on classifying gradings on simple finite-dimensional Lie algebras over algebraically closed
Now let K denote an algebraically closed
field of characteristic 0 with K[x] the corresponding polynomial ring and
The equation (24) admits certainly a solution, in the body C algebraically closed
. Consequently, the number p will be complex.
Let n be a positive integer, and let V be a 2n-dimensional vector space over an algebraically closed
field K of characteristic 0.
Thus we may assume that R is centrally closed over C which is either finite or algebraically closed
and f(x, y) = 0 for all x, y [member of] R.