# On the separability of the partial skew groupoid ring

@article{Bagio2017OnTS,
title={On the separability of the partial skew groupoid ring},
author={Dirceu Bagio and H. Pinedo},
journal={S{\~a}o Paulo Journal of Mathematical Sciences},
year={2017},
volume={11},
pages={370-384}
}
• Published 2017
• Mathematics
• São Paulo Journal of Mathematical Sciences
Given a partial (resp. a global) action $$\alpha$$α of a connected finite groupoid $$\mathscr {G}$$G on a ring $$\mathcal {A},$$A, we determine necessary and sufficient conditions for the partial (resp. the global) skew groupoid ring $$\mathcal {A}\star _\alpha \mathscr {G}$$A⋆αG to be a separable extension of $$\mathcal {A}$$A.
12 Citations
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• 2019
Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A\star_{\alpha}\mathcal{G}$ canExpand
Artinian and noetherian partial skew groupoid rings
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• 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 theExpand
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In this paper, we are interested in the study of the existence of connections between partial groupoid actions and partial group actions. Precisely, we prove that there exists a datum connecting aExpand
On partial skew groupoid rings
• Computer Science, Mathematics
• Int. J. Algebra Comput.
• 2021
Given a partial action α of a connected groupoid 𝒢 on an associative ring A we investigate under what conditions the partial skew groupoid ring A ⋆α𝒢 can be realized as a partial skew group ring.Expand
Isomorphism Theorems for Groupoids and Some Applications
• Mathematics, Computer Science
• Int. J. Math. Math. Sci.
• 2020
Inspired by the Ehresmann-Schein-Nambooripad theorem, a result of R. Exel concerning a one-to-one correspondence between partial actions of groups and actions of inverse semigroups is improved. Expand
Recent developments around partial actions
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• Mathematics
• 2018
In this paper, we introduce the concept of partial groupoid actions on R-semicategories as well as we give criteria for existence of a globalization of it. This point of view is a generalization of...
Ring theoretic properties of partial skew groupoid rings with applications to Leavitt path algebras
• Mathematics
• 2021
Let α = (Ag, αg)g∈G be a group-type partial action of a connected groupoid G on a ring A = ⊕ z∈G0 Az and B := A ⋆α G the corresponding partial skew groupoid ring. In the first part of this paper weExpand
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• 2020
We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$.Expand
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• 2020
Abstract We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal)Expand

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