Let $L_{m,c}$ stand for the free metabelian nilpotent Lie algebra of class $c$ rank $m$ over a field $K$ characteristic zero.
 Automorphisms form $\varphi(x_i)=e^{adu_i}(x_i)$ are called pointwise inner, where $e^{adu_i}$, is inner automorphism
 induced by element $u_i\in L_{m,c}$ each $i=1,\ldots,m$. In present study, we investigate group structure of
 $\text{\rm PInn}(L_{m,c})$...

We prove a conjecture made by Brundan and Kleshchev on the nilpotency degree of cyclotomic quotients of rings that categorify one-half of quantum sl(k).

A one-dimensional cellular automaton is a dynamical system which consisting in a juxtaposition of cells whose state changes over discrete time according to that of their neighbors. One of its simplest behaviors is nilpotency: all configurations of cells are mapped after a finite time into a given “null” configuration. Our main result is that nilpotency is equivalent to the condition that all co...

‡ Every function on a finite residue class ring D/I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a finite commutative local ring with maximal ideal P of nilpotency N satisfying for all a, b∈R, if ab∈ P then a∈ P k , b∈ P j with k+ j ≥min(n,N), we determine the number of functions (as...

We introduce left and right series of semi-braces. This allows to define nilpotent study the structure such semi-braces generalize some results, known for skew braces, B that set additive idempotents E is an ideal . Finally we concept a semi-brace show multiplicative group nilpotent.