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Subalgebras of finite codimension
Mathematical Notes of the Academy of Sciences of the USSR, 1969We consider a commutative algebra A over a field K whose algebraic closure is a finite extension of K, and describe the subalgebras of A that are of finite codimension. We solve a similar problem for the closed subalgebras of Banach algebras.
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BOUNDEDNESS FOR CODIMENSION TWO SUBVARIETIES
International Journal of Mathematics, 2002We prove that for certain projective varieties V ⊂ Pr (e.g. smooth complete intersections with dim (V) ≥ 4, or complete intersections with dim (V) ≥ 7 and codim V ( Sing (V)) ≥ 6), there are only finitely many components of the Hilbert scheme parametrizing irreducible, smooth, projective, codimension two subvarieties of V not of general type.
CILIBERTO, CIRO, DI GENNARO, VINCENZO
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On Codimensions of Algebras with Involution
2020Let A be an associative algebra with involution ∗ over a field F of characteristic zero. One associates to A, in a natural way, a numerical sequence \(c^{\ast }_n(A),\)n = 1, 2, …, called the sequence of ∗-codimensions of A which is the main tool for the quantitative investigation of the polynomial identities satisfied by A.
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2019
The study of isometric immersions becomes increasingly difficult for higher values of the codimension. Therefore, it is important to investigate whether the codimension of an isometric immersion into a space of constant sectional curvature can be reduced.
Marcos Dajczer, Ruy Tojeiro
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The study of isometric immersions becomes increasingly difficult for higher values of the codimension. Therefore, it is important to investigate whether the codimension of an isometric immersion into a space of constant sectional curvature can be reduced.
Marcos Dajczer, Ruy Tojeiro
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A note on bounded codimensions
1990Assume \(R\) is a PI algebra over a field of characteristic zero and \(c_ n(R)\), \(n=1,2,\dots\) is the sequence of codimensions of the \(T\)-ideal of \(R\). Making use of some facts of the representations of the symmetric groups the author establishes the following result. If \(c_ n(R) \leq 1\) for some \(n\) then either \(R\) is nilpotent, \(R^{n+1}
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