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Title2-Generated nilpotent algebras and Eggert
Author(s) Miroslav Korbelář
TypeArticle in Journal
AbstractLet A be a commutative nilpotent finitely-dimensional algebra over a field F of characteristic p > 0 . A conjecture of Eggert (1971) [4] says that p ⋅ dim A ( p ) ⩽ dim A , where A ( p ) is the subalgebra of A generated by elements a p , a ∈ A . We show that the conjecture holds if A ( p ) is at most 2-generated. We give a complete characterization of 2-generated nilpotent commutative algebras in the terms of standard basis with respect to the reverse lexicographical ordering.
KeywordsNilpotent algebra, Eggert
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869310002176
LanguageEnglish
JournalJournal of Algebra
Volume324
Number7
Pages1558 - 1576
Year2010
Edition0
Translation No
Refereed No
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