The Resource Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book)
Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book)
Resource Information
The item Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This book presents a graduatelevel course on modern algebra. It can be used as a teaching book {u2013} owing to the copious exercises {u2013} 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{u2013}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 stepbystep 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 curiositydriven appendices for the selfmotivated student
 Language
 eng
 Extent
 XXII, 539 p. 6 illus.
 Contents

 Basics
 Basic Combinatorial Principles of Algebra
 Review of Elementary Group Properties
 Permutation Groups and Group Actions
 Normal Structure of Groups
 Generation in Groups
 Elementary Properties of Rings
 Elementary properties of Modules
 The Arithmetic of Integral Domains
 Principal Ideal Domains and Their Modules
 Theory of Fields
 Semiprime Rings
 Tensor Products
 Isbn
 9783319197340
 Label
 Algebra : A Teaching and Source Book
 Title
 Algebra
 Title remainder
 A Teaching and Source Book
 Statement of responsibility
 by Ernest Shult, David Surowski
 Language
 eng
 Summary
 This book presents a graduatelevel course on modern algebra. It can be used as a teaching book {u2013} owing to the copious exercises {u2013} 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{u2013}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 stepbystep 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 curiositydriven appendices for the selfmotivated student
 http://library.link/vocab/creatorName
 Shult, Ernest
 Dewey number
 512.46
 Image bit depth
 0
 LC call number
 QA251.5
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorDate
 1949
 http://library.link/vocab/relatedWorkOrContributorName
 Surowski, David
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Field theory (Physics)
 Group theory
 Label
 Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Basics  Basic Combinatorial Principles of Algebra  Review of Elementary Group Properties  Permutation Groups and Group Actions  Normal Structure of Groups  Generation in Groups  Elementary Properties of Rings  Elementary properties of Modules  The Arithmetic of Integral Domains  Principal Ideal Domains and Their Modules  Theory of Fields  Semiprime Rings  Tensor Products
 Control code
 9783319197340
 Dimensions
 unknown
 Extent
 XXII, 539 p. 6 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319197340
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319197340
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Reproduction note
 Electronic resource.
 Specific material designation
 remote
 Label
 Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Basics  Basic Combinatorial Principles of Algebra  Review of Elementary Group Properties  Permutation Groups and Group Actions  Normal Structure of Groups  Generation in Groups  Elementary Properties of Rings  Elementary properties of Modules  The Arithmetic of Integral Domains  Principal Ideal Domains and Their Modules  Theory of Fields  Semiprime Rings  Tensor Products
 Control code
 9783319197340
 Dimensions
 unknown
 Extent
 XXII, 539 p. 6 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319197340
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319197340
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Reproduction note
 Electronic resource.
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/AlgebraATeachingandSourceBookbyErnest/gPua67pVcY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/AlgebraATeachingandSourceBookbyErnest/gPua67pVcY/">Algebra : A Teaching and Source Book, by Ernest Shult, David Surowski, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>