Abstract We explicitly construct a dynamically incoherent partially hyperbolic endomorphisms of $${{\,\mathrm{\mathbb {T}}\,}}^2$$ T 2 in the homotopy class any linear expanding map with integer eigenvalues. These examples exhibit b...

These are notes of two talks with the aim of giving some basic properties of the endomorphism ring of an Abelian variety A and its representations on certain linear objects associated to A. The results can be found in § 5.1 of Shimura’s book [1], but presented in a completely different way. For completeness, we state some definitions. An Abelian variety over a field k is a proper, smooth, conne...

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in categorical tilting context beyond. In n-tilting–cotilting correspondence situation, if $$\mathsf A$$ is a Grothendieck abelian category related B$$ equivalent contramodules over topological ring $$\mathfrak R$$ belonging one certain four classes rings (e. g., commutative), then l...

Abstract Let $X$ be an abelian variety over algebraically closed field $\textbf{k}$ and $f$ a quasi-unipotent automorphism of $X$. When is the complex numbers, Lin, Oguiso, D.-Q. Zhang provide explicit formula for polynomial volume growth (or equivalently, Gelfand–Kirillov dimension twisted homogeneous coordinate ring associated with) pair $(X, f)$, by analytic argument. We give algebraic proof...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

The paper presents a construction of the crossed product of a C *-algebra by a semigroup of endomorphisms generated by partial isometries.

Let R be an o-minimal expansion of a divisible ordered abelian group (R, <, +, 0, 1) with a distinguished positive element 1. Then the following dichotomy holds: Either there is a 0-definable binary operation · such that (R, <, +, ·, 0, 1) is an ordered real closed field; or, for every definable function f : R → R there exists a 0-definable λ ∈ {0} ∪ Aut(R, +) with limx→+∞[f(x) − λ(x)] ∈ R. Thi...