Decidability of theories of modules over tubular algebras

Gregory, Lorna ORCID: https://orcid.org/0000-0002-5508-7217 (2021) Decidability of theories of modules over tubular algebras. Proceedings of the London Mathematical Society, 123 (5). pp. 460-497. ISSN 0024-6115

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Abstract

We show that the common theory of all modules over a tubular algebra (over a recursive algebraically closed field) is decidable. This result supports a long standing conjecture of Mike Prest which says that a finite-dimensional algebra (over a suitably recursive field) is tame if and only if its common theory of modules is decidable (Prest, Model theory and modules (Cambridge University Press, Cambridge, 1988)). Moreover, as a corollary, we are able to confirm this conjecture for the class of concealed canonical algebras over algebraically closed fields. Tubular algebras are the first examples of non-domestic algebras which have been shown to have decidable theory of modules. We also correct results in Harland and Prest (Proc. Lond. Math. Soc. (3) 110 (2015) 695–720), in particular, Corollary 8.8 of that paper.

Item Type:	Article
Additional Information:	Funding Information: EPSRC grant EP/K022490/1.
Uncontrolled Keywords:	03c60,03d35,16d90 (secondary),16g60 (primary),mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	19 Oct 2022 00:07
Last Modified:	19 Dec 2024 01:08
URI:	https://ueaeprints.uea.ac.uk/id/eprint/89185
DOI:	10.1112/plms.12403

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