Book Chapter10.1016/S0049-237X(98)80050-5
Chapter 17 Constructive abelian groups
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TL;DR: In this article, the existence problem of constructivizations for the class of abelian groups can be reduced to the same problem for the classes of periodic groups and torsion-free groups.
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Abstract: Publisher Summary This chapter focuses on exposition of basic results of the theory of Constructive Abelian Groups Algorithmic problems in group theory arose before the appearance of a precise concept of an algorithm At the beginning of the 1930's, this concept was made more precise, and the first results of the theory of algorithms were obtained On the basis of these results, Novikov proved the undecidability of the word problem for groups The chapter introduces two important operations over constructive groups It shows that the existence problem of constructivizations for the class of abelian groups can be reduced to the same problem for the classes of periodic groups and torsion-free groups The concept of a “p”-basis introduced by Kulikov has important meaning in the theory of abelian groups A connection between the constructivizability of groups and the existence of a recursive “p”-basis has been discussed From this connection, a criterion for the strong constructivizability of an abelian “p”-group is obtained The chapter discusses model theoretic method in the theory of constructivizable abelian groups, connections between constructivizability and strong constructivizability, constructivizability of subgroups and factor groups, and the arithmetic hierarchy of abelian groups
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References
Theory of Recursive Functions and Effective Computability
TL;DR: If searching for the ebook by Hartley Rogers Theory of Recursive Functions and Effective Computability in pdf format, then you've come to the faithful site, which presented the complete version of this book in PDF, DjVu, doc, ePub, txt forms.
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Theory of Recursive Functions and Effective Computability
Jr. Hartley Rogers
- 22 Apr 1987
TL;DR: In this paper, the authors discuss related theories of recursively enumerable sets, degree of un-solvability and turing degrees in particular, and generalizations of recursion theory.
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Computable algebra, general theory and theory of computable fields.
TL;DR: In this paper, the authors studied a blend of algebra and the theory of recursive functions for the problem of finding a solvable homomorphism in a finite set of generators of the word problem of a finitely generated group.
Effective Procedures in Field Theory
A. Fröhlich,John C. Shepherdson +1 more
TL;DR: This paper sharpen van der Waerden’s result on the non-existence of a general splitting algorithm by constructing a particular explicitly given field which has no splitting algorithm and shows that the results on the existence of a splitting algorithm for a finite extension field does not hold for inseparable extensions.
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