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Good Magma Gradings On Rings
University West, Department of Engineering Science, Divison of Natural Sciences, Surveying and Mechanical Engineering. (PTW)ORCID iD: 0000-0001-6594-7041
2014 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 42, no 12, p. 5357-5373Article in journal (Refereed) Published
Abstract [en]

Suppose that G and H are magmas and that R is a strongly G-graded ring. We show that there is a bijection between the set of good (zero) H-gradings of R and the set of (zero) magma homomorphisms from G to H. Thereby we generalize a result by Dascalescu, Ion, Nastasescu and Rios Montes from group gradings of matrix rings to strongly magma graded rings. We also show that there is an isomorphism between the preordered set of good (zero) H-filters on R and the preordered set of (zero) submagmas of G \times H. These results are applied to category graded rings and, in particular, to the case when G and H are groupoids. In the latter case, we use this bijection to determine the cardinality of the set of good H-gradings on R.

Place, publisher, year, edition, pages
2014. Vol. 42, no 12, p. 5357-5373
Keywords [en]
Category filtered ring, Category graded ring, Magma filtered ring, Magma graded ring, 16W50, 16W70
National Category
Natural Sciences
Research subject
ENGINEERING, Mathematics
Identifiers
URN: urn:nbn:se:hv:diva-3835DOI: 10.1080/00927872.2011.616563ISI: 000337937700018Scopus ID: 2-s2.0-84902664414OAI: oai:DiVA.org:hv-3835DiVA, id: diva2:453721
Available from: 2011-11-03 Created: 2011-11-03 Last updated: 2019-05-10Bibliographically approved

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Lundström, Patrik

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