PARTIAL ACTIONS OF ORDERED GROUPOIDS ON RINGS-Reference-Cited by-同舟云学术

PARTIAL ACTIONS OF ORDERED GROUPOIDS ON RINGS

Published:2010-06 Issue:03 Volume:09 Page:501-517
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

BAGIO DIRCEU¹,FLORES DAIANA²,PAQUES ANTONIO²

Affiliation:

1. Departamento de Matemática, Universidade Federal de Santa Maria, 97105-900, Santa Maria, RS, Brazil

2. Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900, Porto Alegre, RS, Brazil

Abstract

In this paper, we introduce the notion of a partial action of an ordered groupoid on a ring and we construct the corresponding partial skew groupoid ring. We present sufficient conditions under which the partial skew groupoid ring is either associative or unital. Also, we show that there is a one-to-one correspondence between partial actions of an ordered groupoid G on a ring R, in which the domain of each partial bijection is an ideal, and meet-preserving global actions of the Birget–Rhodes expansion G BR of G on R. Using this correspondence, we prove that the partial skew groupoid ring is a homomorphic image of the skew groupoid ring constructed through the Birget–Rhodes expansion.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949881000404X

Reference13 articles.

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