Titlebook: A Course in Constructive Algebra; Ray Mines,Fred Richman,Wim Ruitenburg Book 1988 Springer Science+Business Media New York 1988 Galois th

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Emmanuel Akyeampong,Pashington Obeng report that every polynomial of odd degree has a root, and that there is a digit that occurs infinitely often in the decimal expansion of π. In opposition to this is the constructive view of mathematics, which focuses attention on the dynamic interaction of the individual with the mathematical univ

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Roman Grynberg,Fwasa K. Singogory of abelian groups, which are modules over the integers. The analogue of a finite-dimensional vector space is a finitely presented module over a principal ideal domain. A finitely presented module is given by matrix. In this section we prove some basic facts about matrices over a principal ideal d

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Roman Grynberg,Fwasa K. Singogoin . that are integral over .. If every element of . is integral over ., then we say that . is an . of .. If . is equal to the integral closure of . in ., then we say that . is . .. If . is a field, the word . in the above definitions may be replaced by the word ..

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https://doi.org/10.1007/978-94-009-1637-1on of ., but other definitions have led to proofs. Standard classical proofs of the Hilbert basis theorem are constructive, if by . we mean that every ideal is finitely generated, but only trivial rings are Noetherian in this sense from the constructive point of view. The first proof of a constructi

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R. Delmas,J. P. Lacaux,D. Brocardare .-algebras, then a . from . to . is a ring homomorphism that is also a .-linear transformation. The term ., when applied to a structure S that is a vector space over ., like a .-algebra, signifies that S is a finite-dimensional vector space over ..