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.

中文翻译：

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管代数模理论的可判定性

我们证明了管状代数（递归代数闭域）上所有模块的共同理论是可判定的。这个结果支持了 Mike Perst 的一个长期存在的猜想，即有限维代数（在适当的递归域上）是驯服的，当且仅当其共同的模理论是可判定的（Prest，模型理论和模（剑桥大学出版社，剑桥，1988 年））。此外，作为一个推论，我们能够在代数闭域上证实隐蔽正则代数类的这一猜想。管状代数是非国内代数的第一个例子，它们已被证明具有可判定的模理论。我们还更正了 Harland 和 Perst ( Proc. Lond. Math. Soc. (3) 110 (2015) 695-720)，特别是该论文的推论 8.8。