Specific examples of such classes are: the class of rings or the class of

algebraically closed fields.

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 fields.

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.

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.

Throughout this paper K is an

algebraically closed field of characteristic 0.

When X is a non-singular projective variety defined over an

algebraically closed field k of characteristic 0 and G is a connected reductive algebraic group over k, moduli spaces of (semi)stable principal G-bundles over X are known to exist and to be quasi-projective schemes (usually singular).

Let F be a fixed

algebraically closed field of characteristic 0.

Let k be an

algebraically closed field of characteristic 0, let A be a reduced Noetherian k-algebra, and let (M, [nabla]) be a finitely generated torsion free A-module of rank one with a (not necessarily integrable) connection.

He describes local and global duality in the special case of irreducible algebraic varieties of an

algebraically closed base field k in terms of differential forms and their residues.

Keywords abc-theorem; abc-conjecture;

algebraically closed field; Wronskian; Diophantine equations.