Subalgebras of FA-presentable algebras
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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. In contrast, 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.
Cain , A J & Ruskuc , N 2014 , ' Subalgebras of FA-presentable algebras ' Algebra Universalis . DOI: 10.1007/s00012-014-0293-0
© Springer Basel 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s00012-014-0293-0
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