Patrik Nystedt

activity

20132020

most citedSimple Rings and Degree Maps

8 citations · 20 across the 7 of their papers we have counts for

collaborators

18 papers

math.RA2020

Strongly graded Leavitt path algebras

Patrik Lundström, Johan Öinert

Let $R$ be a unital ring, let $E$ be a directed graph and recall that the Leavitt path algebra $L_{R} (E)$ carries a natural $Z$ -gradation. We show that $L_{R} (E)$ is strongly…

math.HO2019

Arc length of function graphs via Taylor's formula

Patrik Nystedt

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subd…

math.HO2019

Poisson's fundamental theorem of calculus via Taylor's formula

Patrik Nystedt

We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is…

math.RA2018

A survey of s-unital and locally unital rings

Patrik Nystedt

We gather some classical results and examples that show strict inclusion between the families of unital rings, rings with enough idempotents, rings with sets of local units, locall…

math.RA2018★ 2 cited

Simplicity of algebras via epsilon-strong systems

Patrik Nystedt

We obtain sufficient criteria for simplicity of systems, that is, rings $R$ that are equipped with a family of additive subgroups $R_{s}$ , for $s \in S$ , where $S$ is a semigroup, sa…

math.RA2018

Epsilon-strongly groupoid graded rings, the Picard inverse category and cohomology

Patrik Nystedt, Johan Öinert, Héctor Pinedo

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the cla…

math.RA2017

Noncommutatively Graded Algebras

Patrik Nystedt

Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded…

math.RA2017★ 7 cited

Simplicity of Ore monoid rings

Patrik Nystedt, Johan Öinert, Johan Richter

Given a non-associative unital ring $R$ , a monoid $G$ and a set $π$ of additive maps $R \to R$ , we introduce the Ore monoid ring $R [π; G]$ , and, in a special case, the diff…

math.RA2017

Group gradations on Leavitt path algebras

Patrik Nystedt, Johan Öinert

Given a directed graph $E$ and an associative unital ring $R$ one may define the Leavitt path algebra with coefficients in $R$ , denoted by $L_{R} (E)$ . For an arbitrary group $G$ , $L_…

math.RA2016

Simple graded rings, non-associative crossed products and Cayley-Dickson doublings

Patrik Nystedt, Johan Öinert

We show that if a non-associative unital ring is graded by a hypercentral group, then the ring is simple if and only if it is graded simple and the center of the ring is a field. T…

math.RA2016★ 2 cited

Von-Neumann finiteness and reversibility in some classes of non-associative algebras

Erik Darpö, Patrik Nystedt

We investigate criteria for von-Neumann finiteness and reversibility in some classes of non-associative algebras. We show that all finite-dimensional alternative algebras, as well…

math.RA2016

Epsilon-strongly graded rings, separability and semisimplicity

Patrik Nystedt, Johan Öinert, Héctor Pinedo

We introduce the class of epsilon-strongly graded rings and show that it properly contains both the class of strongly graded rings and the class of unital partial crossed products.…

math.RA2016

Artinian and noetherian partial skew groupoid rings

Patrik Nystedt, Johan Öinert, Héctor Pinedo

Let $α = {α_{g} : R_{g^{- 1}} \to R_{g}}_{g \in mor (G)}$ be a partial action of a groupoid $G$ on a non-associative ring $R$ and let $S = R ⋆_{α} G$ be the associa…

math.RA2016

Partial Category Actions on Sets and Topological Spaces

Patrik Nystedt

We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization. Thereby, we obtain a simultaneous g…

math.RA2015

Non-associative Ore extensions

Patrik Nystedt, Johan Öinert, Johan Richter

We introduce non-associative Ore extensions, $S = R [X; σ, δ]$ , for any non-associative unital ring $R$ and any additive maps $σ, δ : R \to R$ satisfying $σ (1) = 1$ and $δ(1)=0…

math.RA2014★ 1 cited

Outer partial actions and partial skew group rings

Patrik Nystedt, Johan Öinert

We extend the classicial notion of an outer action $α$ of a group $G$ on a unital ring $A$ to the case when $α$ is a partial action on ideals, all of which have local units. We sho…

math.RA2013

Simple Semigroup Graded Rings

Patrik Nystedt, Johan Öinert

We show that if $R$ is a, not necessarily unital, ring graded by a semigroup $G$ equipped with an idempotent $e$ such that $G$ is cancellative at $e$ , the non-zero elements of $eGe…

math.RA2013★ 8 cited

Simple Rings and Degree Maps

Patrik Nystedt, Johan Öinert

For an extension A/B of neither necessarily associative nor necessarily unital rings, we investigate the connection between simplicity of A with a property that we call A-simplicit…