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Dimensions of nilpotent algebras over fields of prime characteristic

Stack, Cora
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Publication Date
1996-11-01
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Article
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Stack, Cora (1996). Dimensions of nilpotent algebras over fields of prime characteristic. Pacific Journal of Mathematics 176 (1), 263-266
Abstract
In this short paper we consider the conjecture that for a finite dimensional commutative nilpotent algebra M over a perfect field of prime characteristic p, dim M greater than or equal to p dim M((p)) where M(p) is the subalgebra of M generated by x(p), x is an element of M. We prove that for any finite dimensional nilpotent algebra M (not necessarily commutative) over any field of prime characteristic p, dim M greater than or equal to p dim M((p)) for dim M((p)) less than or equal to 2.
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Publisher
Mathematical Sciences Publishers
Publisher DOI
10.2140/pjm.1996.176.263
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Attribution-NonCommercial-NoDerivs 3.0 Ireland