Geodesic
On the Dimension of Nilpotent Algebras
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 483-490

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The Eggert conjecture claims that a finite commutative algebra $R$ over a field of prime characteristic $p$ has the property $\dim R\ge p\dim R^{(1)}$, where $R^{(1)}$ is the subspace of $R$ spanned by the $p$th powers of elements of $R$. We obtain results related to this conjecture and results on nilpotent algebras of rather high nilpotency class. 
@article{MZM_2001_70_4_a0,
     author = {B. Amberg and L. S. Kazarin},
     title = {On the {Dimension} of {Nilpotent} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {483--490},
     publisher = {mathdoc},
     volume = {70},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a0/}
}
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B. Amberg; L. S. Kazarin. On the Dimension of Nilpotent Algebras. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 483-490. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a0/