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arXiv · 1206.5548

Subalgebras of FA-presentable algebras

Alan J. Cain·Nik Ruškuc
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Abstract

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. However, it is proven that a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras, and that the membership problem for such subalgebras is decidable.

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Alan J. Cain, Nik Ruškuc. 2012-06-24. Subalgebras of FA-presentable algebras. https://doi.org/10.1007/s00012-014-0293-0

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