LEADER 03848nam 22005415 450 001 9910254307103321 005 20200703182422.0 010 $a3-319-65235-4 024 7 $a10.1007/978-3-319-65235-1 035 $a(CKB)3710000001631072 035 $a(DE-He213)978-3-319-65235-1 035 $a(MiAaPQ)EBC6315595 035 $a(MiAaPQ)EBC5596500 035 $a(Au-PeEL)EBL5596500 035 $a(OCoLC)1004982105 035 $a(PPN)203853865 035 $a(EXLCZ)993710000001631072 100 $a20170830d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Relation Algebras $eRelation Algebras, Volume 1 /$fby Steven Givant 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XXXII, 572 p. 25 illus.) 311 $a3-319-65234-6 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThe 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 naïve 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. 606 $aLogic, Symbolic and mathematical 606 $aAlgebra 606 $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 615 0$aLogic, Symbolic and mathematical. 615 0$aAlgebra. 615 14$aMathematical Logic and Foundations. 615 24$aGeneral Algebraic Systems. 676 $a511.324 700 $aGivant$b Steven$4aut$4http://id.loc.gov/vocabulary/relators/aut$059680 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254307103321 996 $aIntroduction to Relation Algebras$92174113 997 $aUNINA