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ON ALGEBRAIC CLOSURE IN PSEUDOFINITE FIELDS
, 2009
"... We study the automorphism group of the algebraic closure of a substructure A of a pseudofinite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory, we show that algebraic closure agrees wit ..."
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We study the automorphism group of the algebraic closure of a substructure A of a pseudofinite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory, we show that algebraic closure agrees
About the algebraic closure . . .
"... We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the NewtonPuiseux method. Then we study more ca ..."
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We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the NewtonPuiseux method. Then we study more
CONSTRUCTING ALGEBRAIC CLOSURES
"... Let K be a field. We want to construct an algebraic closure of K, i.e., an algebraic extension of K which is algebraically closed. It will be built out of the quotient of a polynomial ring in a very large number of variables. Let P be the set of all nonconstant monic polynomials in K[X] and let A = ..."
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Let K be a field. We want to construct an algebraic closure of K, i.e., an algebraic extension of K which is algebraically closed. It will be built out of the quotient of a polynomial ring in a very large number of variables. Let P be the set of all nonconstant monic polynomials in K[X] and let A
On manysorted algebraic closure operators
 Mathematische Nachrichten
"... Abstract. A theorem of BirkhoffFrink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the operator that constructs the subalgebra generated by a subset. However, for manysorted sets, i.e., indexed families of sets, such a theorem ..."
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Cited by 3 (3 self)
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Abstract. A theorem of BirkhoffFrink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the operator that constructs the subalgebra generated by a subset. However, for manysorted sets, i.e., indexed families of sets, such a
MATHEMATICS ON THE ALGEBRAIC CLOSURE OF TWO BY
"... (Communicated by Prof. J. H. van Lint at the meeting of January 29, 1977) ..."
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(Communicated by Prof. J. H. van Lint at the meeting of January 29, 1977)
The algebraic closure of the power series field in positive characteristic
 PROC. AMER. MATH. SOC
, 2001
"... For K an algebraically closed field, let K((t)) denote the quotient field of the power series ring over K. The “NewtonPuiseux theorem ” states that if K has characteristic 0, the algebraic closure of K((t)) is the union of the fields K((t 1/n)) over n ∈ N. We answer a question of Abhyankar by con ..."
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Cited by 28 (5 self)
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For K an algebraically closed field, let K((t)) denote the quotient field of the power series ring over K. The “NewtonPuiseux theorem ” states that if K has characteristic 0, the algebraic closure of K((t)) is the union of the fields K((t 1/n)) over n ∈ N. We answer a question of Abhyankar
THE POWER OF MULTIFOLDS: FOLDING THE ALGEBRAIC CLOSURE OF THE RATIONAL NUMBERS
"... ABSTRACT. We define the nparameter multifold and show how to use oneparameter multifolds to get the algebraic closure of the rational numbers. 1. ..."
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ABSTRACT. We define the nparameter multifold and show how to use oneparameter multifolds to get the algebraic closure of the rational numbers. 1.
Power series and padic algebraic closures
 Journal of Number Theory
"... We describe a presentation of the algebraic closure of the ring of Witt vectors of an algebraically closed field of characteristic p> 0. The construction uses “generalized power series in p ” as constructed by Poonen, based on an example of Lampert. 1 ..."
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Cited by 7 (1 self)
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We describe a presentation of the algebraic closure of the ring of Witt vectors of an algebraically closed field of characteristic p> 0. The construction uses “generalized power series in p ” as constructed by Poonen, based on an example of Lampert. 1
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