國立虎尾科技大學 |

Introduction to relation algebras = relation algebras.. Volume 1 /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Introduction to relation algebras/ by Steven Givant.
Reminder of title:	relation algebras.
Author:	Givant, Steven.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	xxxii, 572 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Mathematics. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-65235-1
ISBN:	9783319652351

Introduction to relation algebras = relation algebras.. Volume 1 /
Givant, Steven.

Introduction to relation algebrasrelation algebras.Volume 1 /[electronic resource] :by Steven Givant. - Cham :Springer International Publishing :2017. - xxxii, 572 p. :ill., digital ;24 cm.

Preface -- Introduction -- 1. The calculus of relations -- 2. Relation algebras -- 3. Examples of relation algebras -- 4. Arithmetic -- 5. Special elements -- 6. Subalgebras -- 7. Homomorphisms -- 8. Ideals and quotients -- 9. Simple algebras -- 10. Relativizations -- 11. Direct products -- 12. Subdirect products -- 13. Minimal relation algebras -- References -- Index.

The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naive set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.

ISBN: 9783319652351

Standard No.: 10.1007/978-3-319-65235-1doiSubjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA10

Dewey Class. No.: 511.324

Introduction to relation algebras = relation algebras.. Volume 1 /
LDR:02969nam a2200325 a 4500 001 923766
003 DE-He213
005 20180319145529.0
006 m d
007 cr nn 008maaau
008 190625s2017 gw s 0 eng d
020 $a 9783319652351 $q (electronic bk.)
020 $a 9783319652344 $q (paper)
024 7 $a 10.1007/978-3-319-65235-1 $2 doi
035 $a 978-3-319-65235-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA10
072 7 $a PBC $2 bicssc
072 7 $a PBCD $2 bicssc
072 7 $a MAT018000 $2 bisacsh
082 0 4 $a 511.324 $2 23
090 $a QA10 $b .G539 2017
100 1 $a Givant, Steven. $3 896656
245 1 0 $a Introduction to relation algebras $h [electronic resource] : $b relation algebras. $n Volume 1 / $c by Steven Givant.
260 $a Cham : $c 2017. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxxii, 572 p. : $b ill., digital ; $c 24 cm.
505 0 $a Preface -- Introduction -- 1. The calculus of relations -- 2. Relation algebras -- 3. Examples of relation algebras -- 4. Arithmetic -- 5. Special elements -- 6. Subalgebras -- 7. Homomorphisms -- 8. Ideals and quotients -- 9. Simple algebras -- 10. Relativizations -- 11. Direct products -- 12. Subdirect products -- 13. Minimal relation algebras -- References -- Index.
520 $a The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naive set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the leading authorities in the field. Collecting, curating, and illuminating over 75 years of progress since Tarski's seminal work in 1941, this textbook in two volumes offers a landmark, unified treatment of the increasingly relevant field of relation algebras. Clear and insightful prose guides the reader through material previously only available in scattered, highly-technical journal articles. Students and experts alike will appreciate the work as both a textbook and invaluable reference for the community.
650 0 $a Mathematics. $3 527692
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Logic, Symbolic and mathematical. $3 527823
650 2 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a General Algebraic Systems. $3 672227
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-65235-1
950 $a Mathematics and Statistics (Springer-11649)