Patrik Nystedt

activity

20172020

collaborators

7 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

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…