Algebra

A Teaching and Source Book

Nonfiction, Science & Nature, Mathematics, Group Theory, Algebra
Cover of the book Algebra by David Surowski, Ernest Shult, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: David Surowski, Ernest Shult ISBN: 9783319197340
Publisher: Springer International Publishing Publication: July 14, 2015
Imprint: Springer Language: English
Author: David Surowski, Ernest Shult
ISBN: 9783319197340
Publisher: Springer International Publishing
Publication: July 14, 2015
Imprint: Springer
Language: English

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra.

The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products.

Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra.

The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products.

Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

More books from Springer International Publishing

Cover of the book Stakeholder Theory by David Surowski, Ernest Shult
Cover of the book Semantic Keyword-based Search on Structured Data Sources by David Surowski, Ernest Shult
Cover of the book Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics, Volume 3 by David Surowski, Ernest Shult
Cover of the book Transmitting and Gaining Data by David Surowski, Ernest Shult
Cover of the book Topological Microfluidics by David Surowski, Ernest Shult
Cover of the book Silicon Optoelectronic Integrated Circuits by David Surowski, Ernest Shult
Cover of the book Environmental Assessment of Lightweight Electric Vehicles by David Surowski, Ernest Shult
Cover of the book Human Reliability, Error, and Human Factors in Power Generation by David Surowski, Ernest Shult
Cover of the book Geometry of Manifolds with Non-negative Sectional Curvature by David Surowski, Ernest Shult
Cover of the book Living With Hacktivism by David Surowski, Ernest Shult
Cover of the book Refinement by David Surowski, Ernest Shult
Cover of the book Search for the Higgs Boson in the Vector Boson Fusion Channel at the ATLAS Detector by David Surowski, Ernest Shult
Cover of the book Software Project Management for Distributed Computing by David Surowski, Ernest Shult
Cover of the book Rethinking Resilience, Adaptation and Transformation in a Time of Change by David Surowski, Ernest Shult
Cover of the book Charles Taylor, Michael Polanyi and the Critique of Modernity by David Surowski, Ernest Shult
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy