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Maximal commutative subrings and simplicity of Ore extensions
Lund University.
Lund University.
Mälardalen University, School of Education, Culture and Communication. (Mathematics/Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2013 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, E-ISSN 1793-6829, Vol. 12, no 4, p. Article Number: 1250192-Article in journal (Refereed) Published
Abstract [en]

The aim of this article is to describe necessary and sufficient conditions for simplicity of Ore extension rings, with an emphasis on differential polynomial rings. We show that a differential polynomial ring, R[x;id,δ], is simple if and only if its center is a field and R is δ-simple. When R is commutative we note that the centralizer of R in R[x;σ,δ] is a maximal commutative subring containing R and, in the case when σ=id, we show that it intersects every non-zero ideal of R[x;id,δ] non-trivially. Using this we show that if R is δ-simple and maximal commutative in R[x;id,δ], then R[x;id,δ] is simple. We also show that under some conditions on R the converse holds.

Place, publisher, year, edition, pages
2013. Vol. 12, no 4, p. Article Number: 1250192-
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-17937DOI: 10.1142/S0219498812501927ISI: 000316952300011Scopus ID: 2-s2.0-84874390665OAI: oai:DiVA.org:mdh-17937DiVA, id: diva2:589149
Funder
Swedish Research Council, 20076338Available from: 2013-01-17 Created: 2013-01-17 Last updated: 2018-02-27Bibliographically approved

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Silvestrov, Sergei

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