國立虎尾科技大學 |

Monomial ideals and their decompositions

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Monomial ideals and their decompositions/ by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff.
作者:	Moore, W. Frank.
其他作者:	Rogers, Mark.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xxiv, 387 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Commutative algebra. -
電子資源:	https://doi.org/10.1007/978-3-319-96876-6
ISBN:	9783319968766

Monomial ideals and their decompositions
Moore, W. Frank.

Monomial ideals and their decompositions[electronic resource] /by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff. - Cham :Springer International Publishing :2018. - xxiv, 387 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

-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.

This 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.

ISBN: 9783319968766

Standard No.: 10.1007/978-3-319-96876-6doiSubjects--Topical Terms:

672047
Commutative algebra.

LC Class. No.: QA251.3 / .M667 2018

Dewey Class. No.: 512.44

Monomial ideals and their decompositions
LDR:02620nam a2200337 a 4500 001 929794
003 DE-He213
005 20190326113844.0
006 m d
007 cr nn 008maaau
008 190626s2018 gw s 0 eng d
020 $a 9783319968766 $q (electronic bk.)
020 $a 9783319968742 $q (paper)
024 7 $a 10.1007/978-3-319-96876-6 $2 doi
035 $a 978-3-319-96876-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA251.3 $b .M667 2018
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.44 $2 23
090 $a QA251.3 $b .M825 2018
100 1 $a Moore, W. Frank. $3 1210570
245 1 0 $a Monomial ideals and their decompositions $h [electronic resource] / $c by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxiv, 387 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $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.
520 $a This 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.
650 0 $a Commutative algebra. $3 672047
650 0 $a Polynomials. $3 528565
650 0 $a Decomposition (Mathematics) $3 672292
650 1 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Symbolic and Algebraic Manipulation. $3 669944
650 2 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Algebraic Topology. $3 672209
650 2 4 $a Algebraic Geometry. $3 670184
700 1 $a Rogers, Mark. $3 1027964
700 1 $a Sather-Wagstaff, Sean. $3 1210571
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Universitext. $3 881573
856 4 0 $u https://doi.org/10.1007/978-3-319-96876-6
950 $a Mathematics and Statistics (Springer-11649)