Search results for "Almost nilpotent"
showing 3 items of 3 documents
Codimension and colength sequences of algebras and growth phenomena
2015
We consider non necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe some of the results obtained in recent years on the sequence of codimensions and the sequence of colengths of an algebra.
On almost nilpotent varieties of subexponential growth
2015
Abstract Let N 2 be the variety of left-nilpotent algebras of index two, that is the variety of algebras satisfying the identity x ( y z ) ≡ 0 . We introduce two new varieties, denoted by V sym and V alt , contained in the variety N 2 and we prove that V sym and V alt are the only two varieties almost nilpotent of subexponential growth.
On Almost Nilpotent Varieties of Linear Algebras
2020
A variety \(\mathcal {V}\) is almost nilpotent if it is not nilpotent but all proper subvarieties are nilpotent. Here we present the results obtained in recent years about almost nilpotent varieties and their classification.