Finite and Infinite Primes for Rings and Fields PDF Download
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Author: David Harrison
Publisher: American Mathematical Soc.
ISBN: 0821812688
Category : Algebraic fields
Languages : en
Pages : 66
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Book Description
Author: David Harrison
Publisher: American Mathematical Soc.
ISBN: 0821812688
Category : Algebraic fields
Languages : en
Pages : 66
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Book Description
Author: Shahriar Shahriar
Publisher: American Mathematical Soc.
ISBN: 1470428490
Category : Mathematics
Languages : en
Pages : 698
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Book Description
This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Author: J. Alajbegovic
Publisher: Springer Science & Business Media
ISBN: 9401127166
Category : Mathematics
Languages : en
Pages : 339
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Book Description
Various types of approximation theorems are frequently used in general commutative algebra, and they have been found to be useful tools in valuation theory, the theory of Abelian lattice ordered groups, multiplicative ideal theory, etc. Part 1 of this volume is devoted to the investigation of approximation theorems from a classical point of view. The chapters of this part deal with fields and rings, partly ordered groups, and with multirings and d-groups. Part II investigates approximation theorems from a general, categorical point of view. This part is essentially self-contained and requires only a basic knowledge of category theory and first-order logic. For researchers and graduate students of commutative algebra, category theory, as well as applications of logic.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 186
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Book Description
Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Author: Tsit-Yuen Lam
Publisher: American Mathematical Soc.
ISBN: 0821807021
Category : Mathematics
Languages : en
Pages : 158
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Book Description
Presents an introduction to ordered fields and reduced quadratic forms using valuation-theoretic techniques. This book describes the techniques of residue forms and the relevant Springer theory.
Author: G. Betsch
Publisher: Elsevier
ISBN: 0080872484
Category : Mathematics
Languages : en
Pages : 313
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Book Description
Most topics in near-ring and near-field theory are treated here, along with an extensive introduction to the theory.There are two invited lectures: ``Non-Commutative Geometry, Near-Rings and Near-Fields'' which indicates the relevance of near-rings and near-fields for geometry, while ``Pseudo-Finite Near-Fields'' shows the impressive power of model theoretic methods. The remaining papers cover such topics as D.G. near-rings, radical theory, KT-near-fields, matrix near-rings, and applications to systems theory.
Author: Renata Scognamillo
Publisher: Springer
ISBN: 8876425012
Category : Mathematics
Languages : en
Pages : 125
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Book Description
The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert’s Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.
Author: F. J. van der Linden
Publisher:
ISBN:
Category : Algebraic fields
Languages : en
Pages : 222
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Book Description
Author: Alexandra Shlapentokh
Publisher: Cambridge University Press
ISBN: 9780521833608
Category : Mathematics
Languages : en
Pages : 342
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Book Description
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