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Group gradations on Leavitt path algebras.
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 viewedExpand
Artinian and noetherian partial skew groupoid rings
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 theExpand
Simple semigroup graded rings
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 andExpand
Partial category actions on sets and topological spaces
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 simultaneousExpand
Epsilon-strongly graded rings, separability and semisimplicity
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 determineExpand
Noncommutatively Graded Algebras
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 theExpand
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
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 classicalExpand
Simple rings and degree maps
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 $B$. ByExpand
Von-Neumann Finiteness and Reversibility in some Classes of Non-Associative Algebras
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 algebrasExpand
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