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dc.contributor.authorMayr, Peter
dc.contributor.authorRuskuc, Nik
dc.identifier.citationMayr , P & Ruskuc , N 2019 , ' Generating subdirect products ' , Journal of the London Mathematical Society , vol. 100 , no. 2 , pp. 404-424 .
dc.identifier.otherPURE: 258212498
dc.identifier.otherPURE UUID: 0c1cb3d4-e642-4d56-be64-52f849030650
dc.identifier.otherScopus: 85064057260
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702076
dc.identifier.otherWOS: 000488367700003
dc.descriptionThe first author was supported by the National Science Foundation under Grant No. DMS 1500254.en
dc.description.abstractWe study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove general results for arbitrary congruence permutable varieties, which generalize previously known results for groups, and which apply to modules, rings, K-algebras and loops. For instance, if C is a fiber product of A and B over a common quotient D, and if A, B and D are finitely presented, then C is finitely generated. For subdirect products of more than two factors we establish a general connection with projections on pairs of factors and higher commutators. More detailed results are provided for groups, loops, rings and K-algebras. In particular, let C be a subdirect product o fK-algebras A1, · · · , An for a Noetherian ring K such that the projection of C onto any Ai × Aj has finite co-rank in Ai × Aj. Then C is finitely generated (respectivley, finitely presented) if and only if all Ai are finitely generated (respectively, finitely presented). Finally, examples of semigroups and lattices are provided which indicate further complications as one ventures beyond congruence permutable varieties
dc.relation.ispartofJournal of the London Mathematical Societyen
dc.rightsCopyright © 2019 London Mathematical Society. This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at
dc.subjectQA Mathematicsen
dc.titleGenerating subdirect productsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.description.statusPeer revieweden

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