Progress in Commutative Algebra 2. Closures, Finiteness and Factorization
This is the second 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...
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| Príomhchruthaitheoirí: | , , , |
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| Formáid: | Online |
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De Gruyter
2021
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| Ábhair: | |
| Rochtain ar líne: | 33197 |
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Níl clibeanna ann, Bí ar an gcéad duine le clib a chur leis an taifead seo!
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| _version_ | 1869515733382201344 |
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| author | Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. Sather-Wagstaff, Sean M. |
| author_browse | Francisco, Christopher Klingler, Lee C. Sather-Wagstaff, Sean M. Vassilev, Janet C. |
| author_facet | Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. Sather-Wagstaff, Sean M. |
| author_sort | Francisco, Christopher |
| collection | Directory of Open Access Books |
| description | This is the second 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 surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely |
| format | Online |
| id | doab-20.500.12854ir-57156 |
| 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-571562023-12-20T18:40:33Z Progress in Commutative Algebra 2. Closures, Finiteness and Factorization Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. Sather-Wagstaff, Sean M. QA1-939 Closure Commutative Algebra Decomposition Factorization bic Book Industry Communication::P Mathematics & science This is the second 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 surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely 2021-02-12T00:09:18Z 2021-02-12T00:09:18Z 2019-04-25 11:21:03 2012 book 33197 9783110278606 https://directory.doabooks.org/handle/20.500.12854/57156 eng De Gruyter Proceedings in Mathematics image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://doi.org/10.1515/9783110278606 De Gruyter 10.1515/9783110278606 10.1515/9783110278606 af2fbfcc-ee87-43d8-a035-afb9d7eef6a5 969f21b5-ac00-4517-9de2-44973eec6874 9783110278606 325 102373 Knowledge Unlatched open access |
| spellingShingle | QA1-939 Closure Commutative Algebra Decomposition Factorization bic Book Industry Communication::P Mathematics & science Francisco, Christopher Vassilev, Janet C. Klingler, Lee C. Sather-Wagstaff, Sean M. Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title | Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title_full | Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title_fullStr | Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title_full_unstemmed | Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title_short | Progress in Commutative Algebra 2. Closures, Finiteness and Factorization |
| title_sort | progress in commutative algebra 2 closures finiteness and factorization |
| topic | QA1-939 Closure Commutative Algebra Decomposition Factorization bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 Closure Commutative Algebra Decomposition Factorization bic Book Industry Communication::P Mathematics & science |
| url | 33197 |
| work_keys_str_mv | AT franciscochristopher progressincommutativealgebra2closuresfinitenessandfactorization AT vassilevjanetc progressincommutativealgebra2closuresfinitenessandfactorization AT klinglerleec progressincommutativealgebra2closuresfinitenessandfactorization AT satherwagstaffseanm progressincommutativealgebra2closuresfinitenessandfactorization |