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Finite automata and algebraic extensions of function fields

Kiran S. Kedlaya (2006)

Journal de Théorie des Nombres de Bordeaux

We give an automata-theoretic description of the algebraic closure of the rational function field 𝔽 q ( t ) over a finite field 𝔽 q , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over 𝔽 q . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base p expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...

Finite dimensional rings of quotients.

H. Leroy Hutson (1993)

Publicacions Matemàtiques

In this paper we characterize commutative rings with finite dimensional classical ring of quotients. To illustrate the diversity of behavior of these rings we examine the case of local rings and FPF rings. Our results extend earlier work on rings with zero-dimensional rings of quotients.

Finite mutation classes of coloured quivers

Hermund André Torkildsen (2011)

Colloquium Mathematicae

We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.

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