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 order to find a suitable expression of an arbitrary square matrix over finite commutative ring, we prove that every such is always representable as sum potent and nilpotent at most two when the Jacobson radical ring has zero-square. This somewhat extends results ours in Linear Multilinear Algebra (2022) established for matrices considered on fields. Our main theorem also improves recent due ...

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...

I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs (A,B) commuting nilpotent operators on a vector space contains an arbitrary t-tuple linear operators. Moreover, it representations quiver finite-dimensional algebra, so is considered as hopeless. If such pair, then KerA?KerB?0. We give simple normal form (Anor,Bnor) matrices if KerA?KerB one-dimensional. do not ...

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 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.

If F is an algebraically closed field, any element in M n (F) is similar to a sum of a diagonal matrix and a nilpotent matrix whose non-zero entries are all 1, just above the diagonal. Something similar is true for elements of an arbitrary affine algebraic group as well as its Lie algebra. That's what this essay will attempt to explain. I begin with a very elementary account of what happens for...