We prove that a Lie nilpotent one-sided ideal of an associative ring R is contained in a Lie solvable two-sided ideal of R. An estimation of derived length of such Lie solvable ideal is obtained depending on the class of Lie nilpotency of the Lie nilpotent one-sided ideal of R. One-sided Lie nilpotent ideals contained in ideals generated by commutators of the form [. . . [[r1, r2], . . .], rn−1...

Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.

In the recent progress [BE1], [Me] and [Z2], the wellknown JC (Jacobian conjecture) ([BCW], [E]) has been reduced to a VC (vanishing conjecture) on the Laplace operators and HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent). In this paper, we first show the vanishing conjecture above, hence also the JC, is equivalent to a vanishing conjecture for all 2nd or...

Superfield constraints were often used in the past, in particular to describe the AkulovVolkov action of the goldstino by a superfield formulation with L=(ΦΦ)D+[(fΦ)F+h.c.] endowed with the nilpotent constraint Φ = 0 for the goldstino superfield (Φ). Inspired by this, such constraint is often used to define the goldstino superfield even in the presence of additional superfields, for example in ...

Maximal and minimal conditions for ideals in associative rings have often been considered, but little seems to be known of these conditions in non-associative rings, or of chain conditions on the non-normal subgroups of a group. Moreover, it is usual to assume the condition for one-sided ideals in noncommutative rings, and the weaker condition for two-sided ideals rarely appears. In this note w...

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.

let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.

We give a definition of nilpotent association schemes as a generalization of nilpotent groups and investigate their basic properties. Moreover, for a group-like scheme, we characterize the nilpotency by its character products.