Progress in Commutative Algebra 1. Combinatorics and Homology
This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra a...
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De Gruyter
2021
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| author | Sather-Wagstaff, Sean Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. |
| author_browse | Francisco, Christopher Klingler, Lee C. Sather-Wagstaff, Sean Vassilev, Janet C. |
| author_facet | Sather-Wagstaff, Sean Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. |
| author_sort | Sather-Wagstaff, Sean |
| collection | Directory of Open Access Books |
| description | This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological art |
| format | Online |
| id | doab-20.500.12854ir-57155 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | De Gruyter |
| publisherStr | De Gruyter |
| record_format | ojs |
| spelling | doab-20.500.12854ir-571552023-12-20T18:40:35Z Progress in Commutative Algebra 1. Combinatorics and Homology Sather-Wagstaff, Sean Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. QA1-939 Commutative Algebra Homology Combinatorics bic Book Industry Communication::P Mathematics & science This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological art 2021-02-12T00:09:15Z 2021-02-12T00:09:15Z 2019-04-25 11:21:03 2012 book 33198 9783110250404 https://directory.doabooks.org/handle/20.500.12854/57155 eng De Gruyter Proceedings in Mathematics image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://doi.org/10.1515/9783110250404 De Gruyter 10.1515/9783110250404 10.1515/9783110250404 af2fbfcc-ee87-43d8-a035-afb9d7eef6a5 969f21b5-ac00-4517-9de2-44973eec6874 9783110250404 372 102374 Knowledge Unlatched open access |
| spellingShingle | QA1-939 Commutative Algebra Homology Combinatorics bic Book Industry Communication::P Mathematics & science Sather-Wagstaff, Sean Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. Progress in Commutative Algebra 1. Combinatorics and Homology |
| title | Progress in Commutative Algebra 1. Combinatorics and Homology |
| title_full | Progress in Commutative Algebra 1. Combinatorics and Homology |
| title_fullStr | Progress in Commutative Algebra 1. Combinatorics and Homology |
| title_full_unstemmed | Progress in Commutative Algebra 1. Combinatorics and Homology |
| title_short | Progress in Commutative Algebra 1. Combinatorics and Homology |
| title_sort | progress in commutative algebra 1 combinatorics and homology |
| topic | QA1-939 Commutative Algebra Homology Combinatorics bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 Commutative Algebra Homology Combinatorics bic Book Industry Communication::P Mathematics & science |
| url | 33198 |
| work_keys_str_mv | AT satherwagstaffsean progressincommutativealgebra1combinatoricsandhomology AT franciscochristopher progressincommutativealgebra1combinatoricsandhomology AT vassilevjanetc progressincommutativealgebra1combinatoricsandhomology AT klinglerleec progressincommutativealgebra1combinatoricsandhomology |