Related papers: Semiartinian profinite algebras have nilpotent Jac…

Let $H$ be a subgroup of $\text{Sym}_n$, the symmetric group of degree $n$. For a fixed integer $l \geq 2$, the group $G$ presented with generators $x_1, x_2, \ldots ,x_n$ and with relations $x_{i_1}x_{i_2}\cdots x_{i_l} =x_{\sigma (i_1)}…

We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson…

Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…

This paper shows that a Poisson algebra is nilpotent if and only if it is both associative and Lie nilpotent and examines various properties of the nilradical and the solvable radical. It introduces a basic Frattini theory for dialgebras…

We give a positive answer to a conjecture of Faith stating that a self-injective semiprimary ring is QF, for algebras which are at most countable dimensional modulo their Jacobson radical. As a consequence of the method used, we also give…

In the present work we introduce notions such as $k$-solvability, $s$- and $K_1$-nilpotency and the corresponding radicals. We prove that these radicals are invariant under derivations of Leibniz $n$-algebras. The Frattini and Cartan…

Let $B$ be a finitely generated algebra over a field $k$. Then $B$ is called a Jacobson algebra if every semiprime ideal of $B$ is semiprimitive. We will discuss several conditions, all involving the commutant of simple $B$-modules, which…

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…

We prove that a profinite algebra whose left (right) cyclic modules are torsionless is finite dimensional and QF. We give a relative version of the notion of left (right) PF ring for pseudocompact algebras and prove it is left-right…

Nilpotent Leibniz algebras with isomorphic maximal subalgebras are considered. The algebras are classified for coclass zero, one, and two. The results are field dependent.

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups $(\beta S, \Box)$, where $S$ is a cancellative, countable, abelian semigroup and $\beta S$ is its…

We study canonical filtrations of finite-dimensional associative algebras and Lie algebras. These filtrations are defined via optimal destabilizing one-parameter subgroups in the sense of geometric invariant theory (GIT), and appear to be a…

We say that a ring is strongly (resp. weakly) left Jacobson if every semiprime (resp. prime) left ideal is an intersection of maximal left ideals. There exist Jacobson rings that are not weakly left Jacobson, e.g. the Weyl algebra. Our main…

A classical result of topological algebra states that any compact left topological semigroup has an idempotent. We refine this by showing that any compact left topological left semiring has a common, i.e. additive and multiplicative…

The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case. Then the case of split nilradical is worked out.…

We study finite dimensional semisimple Hopf algebra actions on noetherian connected graded Artin-Schelter regular algebras, and introduce definitions of the Jacobian, the reflection arrangement and the discriminant in a noncommutative…

We prove that an integral Jacobson radical ring is always nil, which extends a well known result from algebras over fields to rings. As a consequence we show that if every element x of a ring R is a zero of some polynomial p_x with integer…

We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…

We prove two approximations of the open problem of whether the adjoint group of a non-nilpotent nil ring can be finitely generated: We show that the adjoint group of a non-nilpotent Jacobson radical cannot be boundedly generated, and on the…

The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…