PI ORE EXTENSIONS 3 1 Preliminaries

Ore extensions of skew $pi$-Armendariz rings

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

Polynomial Ore Extensions of Baer and p.p.-Rings

Uniqueness of Traveling Waves for a Two-Dimensional Bistable Periodic Lattice Dynamical System

and Applied Analysis 3 This paper is organized as follows. In Section 2, we give some preliminaries including a comparison principle. Then we prove uniqueness of traveling wave with nonzero speed in Section 3. 2. Preliminaries The following lemma can be easily deduced from 1.5 and 1.6 . Lemma 2.1. Let {ui,j}i,j∈Z be a solution of 1.1 – 1.6 . If c > 0 < 0 , then ui,j t → 0 → 1 as t → ∞ and ui,j ...

Double Ore Extensions versus Iterated Ore Extensions

Motivated by the construction of new examples of Artin-Schelter regular algebras of global dimension four, J.J.Zhang and J.Zhang (2008) introduced an algebra extension AP [y1, y2;σ, δ, τ ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this paper is to describe those double Ore extensions whic...

Pseudo linear transformations and evaluation in Ore extensions

The relations between evaluation of Ore polynomials and pseudo-linear transformations are studied. The behavior of these transformations under homomorphisms of Ore extensions, in particular with respect to algebraicity, is analyzed leading to characterization of left and right primitivity of an Ore extension. Necessary and sufficient conditions are given for algebraic pseudo-linear transformati...