LEADER 04732nam 22008055 450 001 9910300125503321 005 20200704033844.0 010 $a3-319-96876-9 024 7 $a10.1007/978-3-319-96876-6 035 $a(CKB)4100000007110875 035 $a(DE-He213)978-3-319-96876-6 035 $a(MiAaPQ)EBC6209515 035 $a(PPN)231457359 035 $a(EXLCZ)994100000007110875 100 $a20181024d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMonomial Ideals and Their Decompositions /$fby W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIV, 387 p. 55 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-96874-2 327 $a-Introduction -- 1. Fundamental Properties of Monomial Ideals . -2. Operations on Monomial Ideals -- 3. M-Irreducible Ideals and Decompositions -- 4. Connections with Combinatorics -- 5. Connections with Other Areas. -6. Parametric Decompositions of Monomial Ideals -- 7. Computing M-Irreducible Decompositions -- Appendix A. Foundational Concepts -- Appendix B. Introduction to Macaulay2 -- Bibliography -- Index. . 330 $aThis textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in abstract algebra that includes polynomial rings and ideals, this book serves as a core text for a course in combinatorial commutative algebra or as preparation for more advanced courses in the area. The text contains over 600 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a firsthand introduction to the computer algebra system Macaulay2 with tutorials and exercises for most sections of the text, preparing them for significant computational work in the area. Connections to non-monomial areas of abstract algebra, electrical engineering, combinatorics and other areas of mathematics are provided which give the reader a sense of how these ideas reach into other areas. . . 410 0$aUniversitext,$x0172-5939 606 $aCommutative algebra 606 $aCommutative rings 606 $aComputer science?Mathematics 606 $aAssociative rings 606 $aRings (Algebra) 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aAlgebraic topology 606 $aAlgebraic geometry 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aComputer science?Mathematics. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aAlgebraic topology. 615 0$aAlgebraic geometry. 615 14$aCommutative Rings and Algebras. 615 24$aSymbolic and Algebraic Manipulation. 615 24$aAssociative Rings and Algebras. 615 24$aCategory Theory, Homological Algebra. 615 24$aAlgebraic Topology. 615 24$aAlgebraic Geometry. 676 $a512.24 700 $aMoore$b W. Frank$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767850 702 $aRogers$b Mark$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSather-Wagstaff$b Sean$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300125503321 996 $aMonomial Ideals and Their Decompositions$92266036 997 $aUNINA