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.

A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ a...

Yoshizawa investigated when local cohomology modules have an annihilator that does not depend on the choice of defining ideal. In this paper we refine his results and investigate relationship between annihilators restricted flat dimensions.

Let R be a local Noetherian commutative ring. We prove that is an Artinian Gorenstein ring if and only every ideal in trace ideal. discuss when the of module coincides with its double annihilator.

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...