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- W2010391229 abstract "Let F 〈 X 〉 be the free unitary associative algebra over a field F on the set X = { x 1 , x 2 , … } . A vector subspace V of F 〈 X 〉 is called a T-subspace (or a T-space ) if V is closed under all endomorphisms of F 〈 X 〉 . A T -subspace V in F 〈 X 〉 is limit if every larger T -subspace W ≩ V is finitely generated (as a T -subspace) but V itself is not. Recently Brandão Jr., Koshlukov, Krasilnikov and Silva have proved that over an infinite field F of characteristic p > 2 the T -subspace C ( G ) of the central polynomials of the infinite dimensional Grassmann algebra G is a limit T -subspace. They conjectured that this limit T -subspace in F 〈 X 〉 is unique, that is, there are no limit T -subspaces in F 〈 X 〉 other than C ( G ) . In the present article we prove that this is not the case. We construct infinitely many limit T -subspaces R k ( k ⩾ 1 ) in the algebra F 〈 X 〉 over an infinite field F of characteristic p > 2 . For each k ⩾ 1 , the limit T -subspace R k arises from the central polynomials in 2 k variables of the Grassmann algebra G ." @default.
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- W2010391229 date "2012-12-01" @default.
- W2010391229 modified "2023-09-24" @default.
- W2010391229 title "Limit T-subspaces and the central polynomials in n variables of the Grassmann algebra" @default.
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- W2010391229 doi "https://doi.org/10.1016/j.jalgebra.2012.08.008" @default.
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