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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.
Let n be a positive integer, and let V be a 2n-dimensional vector space over an algebraically closed field K 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.
] is an algebraically closed field of characteristic zero.
There are arguments (see ) showing that this is the case when K is an uncountable algebraically closed field.
The approach computes the local Denef- Loeser motivic zeta function of a quasi-ordinary power series of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities.
Let k be an algebraically closed field of characteristic 0.