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Simplicity of Ore monoid rings
Department of Engineering Science, University West, Trollhättan, Sweden.
Blekinge Tekniska Högskola.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.ORCID iD: 0000-0003-3931-7358
2019 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 530, p. 69-85Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2019. Vol. 530, p. 69-85
Keywords [en]
Differential monoid ring; Generalized monoid ring; Iterated Ore extension; Non-associative Ore extension; Ore monoid ring; Outer derivation; Simple ring
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-43129DOI: 10.1016/j.jalgebra.2019.04.003ISI: 000469166400003Scopus ID: 2-s2.0-85064169587OAI: oai:DiVA.org:mdh-43129DiVA, id: diva2:1305626
Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-06-18Bibliographically approved

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