In this paper, we conjecture an extension of the Hilbert basis theorem and the finite
generation of invariants to commutative algebras in symmetric finite tensor categories over …

Let Z< X> be the free unital associative ring freely generated by an infinite countable set
X={x 1, x 2,…}. Define a left-normed commutator [x 1, x 2,…, xn] by [a, b]= ab− ba,[a, b, c]=[[a …

Let F be a field and let F< X> be the free unital associative algebra over F freely generated
by an infinite countable set X={x 1, x 2,…}. Define a left-normed commutator [a 1, a 2,…, an] …

The lower central series invariants M k of an associative algebra A are the two-sided ideals
generated by k-fold iterated commutators; the M k provide a filtration of A. We study the …

Let A be a unital associative ring and let T (k) be the two-sided ideal of A generated by all
commutators [a 1, a 2,…, ak](ai∈ A) where [a 1, a 2]= a 1 a 2− a 2 a 1,[a 1,…, ak− 1, ak]=[[a …

Let Z< X> be the free unital associative ring freely generated by an infinite countable set
X={x 1, x 2,…}. Define a left-normed commutator [a 1, a 2,…, an] inductively by [a, b]= ab …

Let Φ be an arbitrary unital associative and commutative ring. The relatively free Lie
nilpotent algebras with three generators over Φ are studied. The product theorem is proved …

We give an accessible introduction into the theory of lower central series of associative
algebras, exhibiting the interplay between algebra, geometry and representation theory that …

Let K be a unital associative and commutative ring and let K⟨ X⟩ be the free unital
associative K-algebra on a non-empty set X of free generators. Define a left-normed …

Let A be an associative unital algebra, B k its successive quotients of lower central series
and N k the successive quotients of ideals generated by lower central series. The geometric …