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Simplicity of Ore monoid rings
Högskolan Väst, Institutionen för ingenjörsvetenskap, Avdelningen för Matematik, Data- och Lantmäteriteknik.ORCID-id: 0000-0001-6594-7041
Blekinge Institute of Technology, Department of Mathematics and Natural Sciences, Karlskrona, SE-37179, Sweden.
Mälardalen University, Academy of Education, Culture and Communication,Box 883, Västerås, SE-72123, Sweden.
2019 (engelsk)Inngår i: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 530, s. 69-85Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Given a non-associative unital ring R, a monoid G and a set π of additive maps R→R, we introduce the Ore monoid ring R[π;G], and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D-structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids. © 2019 Elsevier Inc.

sted, utgiver, år, opplag, sider
2019. Vol. 530, s. 69-85
HSV kategori
Forskningsprogram
TEKNIK, Matematik
Identifikatorer
URN: urn:nbn:se:hv:diva-13849DOI: 10.1016/j.jalgebra.2019.04.003ISI: 000469166400003Scopus ID: 2-s2.0-85064169587OAI: oai:DiVA.org:hv-13849DiVA, id: diva2:1317963
Tilgjengelig fra: 2019-05-24 Laget: 2019-05-24 Sist oppdatert: 2019-07-24bibliografisk kontrollert

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