On the generators of coordinate algebras of affine ind-varieties
Alexander Chernov

TL;DR
This paper investigates the structure of coordinate rings of affine ind-varieties, revealing that non-algebraic affine ind-varieties have uncountably generated coordinate rings and dense subspaces of countable dimension.
Contribution
It demonstrates that coordinate rings of non-algebraic affine ind-varieties lack countable generators and possess dense subspaces of countable dimension, advancing understanding of their algebraic structure.
Findings
Non-isomorphic affine ind-varieties have uncountably generated coordinate rings.
Coordinate rings contain dense subspaces of countable dimension.
Results differentiate algebraic and non-algebraic affine ind-varieties.
Abstract
In this paper we study the structure of the coordinate ring of an affine ind-variety. We prove that any coordinate ring of an affine ind-variety which is not isomorphic to an affine algebraic variety does not have a countable set of generators. Also we prove that coordinate rings of affine ind-varieties have an everywhere dense subspace of countable dimension.
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