Necessary and sufficient conditions for an Ore extension S = R[x;σ, δ] to be a PI ring are given in the case σ is an injective endomorphism of a semiprime ring R satisfying the ACC on annihilators. Also, for an arbitrary endomorphism τ of R, a characterization of Ore extensions R[x; τ ] which are PI rings is given, provided the coefficient ring R is noetherian.

Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

We associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms projections of a finite-dimensional vector space. A characterization is given of it. This characterization makes this order an order verifying the Jordan-Dedekind chain condition. We give also a property for certain finite families of this order. More precisely, the family of parts in...

We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact sequence for isogenies, Poincaré complete reducibility theorem for log abelian varieties, and the semisimplicity of the endomorphism algebras of log abelian varieti...

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Abstract We present a new deterministic algorithm for constructing homomorphism spaces and endomorphism rings of finite dimensional modules. The modules are given via vertex projective presentations over path algebras and finite dimensional quotients of path algebras. We use the theory of right Gröbner bases to encode modules and to construct appropriate systems of equations for computing homom...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

Let P be a partially ordered set. A function φ : P → P is an endomorphism of P if for every two elements x, y of P , the inequality φ(x) 6 φ(y) holds whenever x 6 y. Obviously, the identity mapping is a (trivial ) endomorphism. Here, however, we will be interested in endomorphisms with an image of size less than |P |, i.e. endomorphisms which are not automorphisms of P . We will refer to them a...