Algebras, Lattices, Varieties, Volume I
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-4295-8 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4295-8 (ISBN)
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Presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is filled with useful illustrations and exercises that solidify the reader's understanding.
This book presents the foundations of a general theory of algebras. Often called ``universal algebra'', this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding.
The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras.
There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
This book presents the foundations of a general theory of algebras. Often called ``universal algebra'', this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding.
The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras.
There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Ralph N. McKenzie, Vanderbilt University, Nashville, TN. George F. McNulty, University of South Carolina, Columbia, SC. Walter F. Taylor, University of Colorado, Boulder, CO.
Basic concepts
Lattices
Unary and binary operations
Fundamental algebraic results
Unique factorization
Bibliography
Additional bibliography
List of errata
Table of notation
Index of names
Index of terms
| Erscheinungsdatum | 18.09.2019 |
|---|---|
| Reihe/Serie | Chelsea Publications |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 835 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-4295-7 / 1470442957 |
| ISBN-13 | 978-1-4704-4295-8 / 9781470442958 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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