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Group gradations on Leavitt path algebras.

- Patrik Nystedt, Johan Öinert
- Mathematics
- 30 March 2017

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 $G$, $L_R(E)$ can be viewed… Expand

Artinian and noetherian partial skew groupoid rings

- Patrik Nystedt, Johan Oinert, H. Pinedo
- Mathematics
- 7 March 2016

Let $\alpha = \{ \alpha_g : R_{g^{-1}} \rightarrow R_g \}_{g \in \textrm{mor}(G)}$ be a partial action of a groupoid $G$ on a non-associative ring $R$ and let $S = R \star_{\alpha} G$ be the… Expand

Simple semigroup graded rings

- Patrik Nystedt, Johan Oinert
- Mathematics
- 15 August 2013

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 nonzero elements of eGe form a hypercentral group and… Expand

Partial category actions on sets and topological spaces

- Patrik Nystedt
- Mathematics
- 24 February 2016

ABSTRACT 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… Expand

Epsilon-strongly graded rings, separability and semisimplicity

- Patrik Nystedt, Johan Oinert, H. Pinedo
- Mathematics
- 24 June 2016

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. We determine… Expand

Noncommutatively Graded Algebras

- Patrik Nystedt
- Mathematics
- 4 October 2017

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

A combinatorial proof of associativity of Ore extensions

- Patrik Nystedt
- Computer Science, Mathematics
- Discret. Math.
- 6 December 2013

EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY

- Patrik Nystedt, Johan Öinert, H. Pinedo
- Mathematics
- Glasgow Mathematical Journal
- 20 May 2018

Abstract 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 classical… Expand

Simple rings and degree maps

- Patrik Nystedt, Johan Oinert
- Mathematics
- 26 March 2013

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 $A$-simplicity of $B$. By… Expand

Von-Neumann Finiteness and Reversibility in some Classes of Non-Associative Algebras

- Erik Darpö, Patrik Nystedt
- Mathematics
- 17 August 2016

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 as all algebras… Expand

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