17 citations · 61 across the 13 of their papers we have counts for
17 papers
Centralizers in non-associative rings with a pseudo-degree function
Johan Richter
This papers studies centralizers of an element, , in the nucleus of a non-associative algebra with a special type of valuation. We prove that the centralizer of is a free mo…
Ideals in hom-associative Weyl algebras
Per Bäck, Johan Richter
We introduce hom-associative versions of the higher order Weyl algebras, generalizing the construction of the first hom-associative Weyl algebras. We then show that the higher orde…
Non-unital Ore extensions
Patrik Lundström, Johan Öinert, Johan Richter
In this article, we study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings , under the hypot…
Simplicity of non-associative skew Laurent polynomial rings
Per Bäck, Johan Richter
We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Öinert.
The hom-associative Weyl algebras in prime characteristic
Per Bäck, Johan Richter
We introduce the first hom-associative Weyl algebras over a field of prime characteristic as a generalization of the first associative Weyl algebra in prime characteristic. First,…
Centralizers in PBW Extensions
Alex Behakanira Tumwesigye, Johan Richter, Sergei Silvestrov
In this article we give a description for the centralizer of the coefficient ring in the skew PBW extension We give an explicit description in the q…
Commutants in crossed product algebras for piecewise constant functions on the real line
Alex Behakanira Tumwesigye, Johan Richter, Sergei Silvestrov
In this paper we consider commutants in crossed product algebras, for algebras of piece-wise constant functions on the real line acted on by the group of integers . The…
Ore extensions for function algebras
Johan Richter, Sergei Silvestrov, Alex Tumwesigye
In this article we consider the Ore extension Algebra for the algebra of functions with finite support on a countable set. We derive explicit formulas for twisted der…
On the hom-associative Weyl algebras
Per Bäck, Johan Richter
The first (associative) Weyl algebra is formally rigid in the classical sense. In this paper, we show that it can however be formally deformed in a nontrivial way when considered a…
Hilbert's basis theorem for non-associative and hom-associative Ore extensions
Per Bäck, Johan Richter
We prove a hom-associative version of Hilbert's basis theorem, which includes as special cases both a non-associative version and the classical associative Hilbert's basis theorem…
Hom-associative Ore extensions and weak unitalizations
Per Bäck, Johan Richter, Sergei Silvestrov
We introduce hom-associative Ore extensions as non-unital, non-associative Ore extensions with a hom-associative multiplication, and give some necessary and sufficient conditions w…
Simplicity of Ore monoid rings
Patrik Nystedt, Johan Öinert, Johan Richter
Given a non-associative unital ring , a monoid and a set of additive maps , we introduce the Ore monoid ring , and, in a special case, the diff…
Non-associative Ore extensions
Patrik Nystedt, Johan Öinert, Johan Richter
We introduce non-associative Ore extensions, , for any non-associative unital ring and any additive maps satisfying and $δ(1)=0…
Centralizers and pseudo-degree functions
Johan Richter
We study centralizers in certain algebras with valuation in order to generalize results by Hellström and Silvestrov on centralizers in graded algebras. We prove that the centralize…
Burchnall-Chaundy theory for Ore extensions
Johan Richter
We begin by reviewing a classical result on the algebraic dependence of commuting elements in Weyl algebras. We proceed by describing generalizations of this result to various clas…
Centralizers in Ore extensions of polynomial rings
Johan Richter, Sergei Silvestrov
In this paper we consider centralizers of single elements in Ore extensions of the ring of polynomials in one variable over a field. We show that they are commutative and finitely…
Maximal commutative subrings and simplicity of Ore extensions
Johan Öinert, Johan Richter, Sergei D. Silvestrov
The aim of this article is to describe necessary and sufficient conditions for simplicity of Ore extension rings, with an emphasis on differential polynomial rings. We show that a…