178 lines
No EOL
6.1 KiB
BibTeX
178 lines
No EOL
6.1 KiB
BibTeX
@article{Shibuta2017,
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title = {Affine semigroup rings are of finite F-representation type},
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volume = {45},
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issn = {0092-7872, 1532-4125},
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url = {https://www.tandfonline.com/doi/full/10.1080/00927872.2017.1313425},
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doi = {10.1080/00927872.2017.1313425},
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pages = {5465--5470},
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number = {12},
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journaltitle = {Communications in Algebra},
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shortjournal = {Communications in Algebra},
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author = {Shibuta, Takafumi},
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urldate = {2026-08-03},
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date = {2017-12-02},
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langid = {english},
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}
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@article{Hochster1976,
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title = {The purity of the Frobenius and local cohomology},
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journal = {Advances in Mathematics},
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volume = {21},
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number = {2},
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pages = {117-172},
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year = {1976},
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issn = {0001-8708},
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doi = {https://doi.org/10.1016/0001-8708(76)90073-6},
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url = {https://www.sciencedirect.com/science/article/pii/0001870876900736},
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author = {Melvin Hochster and Joel L Roberts}
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}
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@article{Yasuda2009,
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title = {On monotonicity of F-blowup sequences},
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volume = {53},
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issn = {0019-2082},
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url = {https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-53/issue-1/On-monotonicity-of-F-blowup-sequences/10.1215/ijm/1264170841.full},
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doi = {10.1215/ijm/1264170841},
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number = {1},
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journaltitle = {Illinois Journal of Mathematics},
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shortjournal = {Illinois J. Math.},
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author = {Yasuda, Takehiko},
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urldate = {2026-08-11},
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date = {2009-01-01},
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}
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@article{Bruns2006,
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title = {On seminormal monoid rings},
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volume = {302},
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rights = {https://www.elsevier.com/tdm/userlicense/1.0/},
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issn = {00218693},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S0021869305006605},
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doi = {10.1016/j.jalgebra.2005.11.012},
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pages = {361--386},
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number = {1},
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journaltitle = {Journal of Algebra},
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shortjournal = {Journal of Algebra},
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author = {Bruns, Winfried and Li, Ping and Römer, Tim},
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urldate = {2026-08-12},
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date = {2006-08},
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langid = {english},
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}
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@incollection{Bruns2005,
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author = {Bruns, Winfried},
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title = {Conic divisor classes over a normal monoid algebra},
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booktitle = {Commutative Algebra and Algebraic Geometry},
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series = {Contemporary Mathematics},
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volume = {390},
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pages = {63--71},
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publisher = {American Mathematical Society},
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location = {Providence, RI},
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year = {2005},
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}
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@incollection{Blickle2013,
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location = {New York, {NY}},
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title = {$p^{-1}$-Linear Maps in Algebra and Geometry},
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isbn = {978-1-4614-5291-1 978-1-4614-5292-8},
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url = {https://link.springer.com/10.1007/978-1-4614-5292-8_5},
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doi = {10.1007/978-1-4614-5292-8_5},
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pages = {123--205},
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booktitle = {Commutative Algebra},
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publisher = {Springer New York},
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author = {Blickle, Manuel and Schwede, Karl},
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editor = {Peeva, Irena},
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urldate = {2026-09-01},
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date = {2013},
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langid = {english},
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}
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@inbook{Leuschke2012,
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url = {https://doi.org/10.1515/9783110250404.293},
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title = {Non-commutative Crepant Resolutions: Scenes From Categorical Geometry},
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booktitle = {Progress in Commutative Algebra 1},
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booktitle = {Combinatorics and Homology},
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author = {Graham J. Leuschke},
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editor = {Christopher Francisco and Lee C. Klingler and Sean Sather-Wagstaff and Janet C. Vassilev},
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publisher = {De Gruyter},
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address = {Berlin, Boston},
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pages = {293--364},
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doi = {doi:10.1515/9783110250404.293},
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isbn = {9783110250404},
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year = {2012},
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lastchecked = {2026-09-02}
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}
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@article{Faber2019,
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title = {Non-commutative resolutions of toric varieties},
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journal = {Advances in Mathematics},
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volume = {351},
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pages = {236-274},
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year = {2019},
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issn = {0001-8708},
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doi = {https://doi.org/10.1016/j.aim.2019.04.021},
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url = {https://www.sciencedirect.com/science/article/pii/S0001870819301823},
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author = {Eleonore Faber and Greg Muller and Karen E. Smith},
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keywords = {Toric variety, Non-commutative resolution, Finite global dimension, Non-commutative crepant resolution, Rings of differential operators, Strong F-regularity},
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abstract = {Let R be the coordinate ring of an affine toric variety. We prove, using direct elementary methods, that the endomorphism ring EndR(A), where A is the (finite) direct sum of all (isomorphism classes of) conic R-modules, has finite global dimension equal to the dimension of R. This gives a precise version, and an elementary proof, of a theorem of Špenko and Van den Bergh implying that EndR(A) has finite global dimension. Furthermore, we show that EndR(A) is a non-commutative crepant resolution if and only if the toric variety is simplicial. For toric varieties over a perfect field k of prime characteristic, we show that the ring of differential operators Dk(R) has finite global dimension.}
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}
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@book{Dummit2004,
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author = {Dummit, David S. and Foote, Richard M.},
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title = {Abstract Algebra},
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edition = {3},
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publisher = {John Wiley \& Sons},
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location = {Hoboken, NJ},
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year = {2004},
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}
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@book{Mollin2008,
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location = {Boca Raton},
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edition = {2nd ed},
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title = {Fundamental number theory with applications},
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isbn = {978-1-4200-6659-3},
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series = {Discrete mathematics and its applications},
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pagetotal = {369},
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publisher = {Chapman \& Hall/{CRC}},
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author = {Mollin, Richard A.},
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date = {2008},
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}
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@book{Nastasescu2004,
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location = {Berlin ; New York},
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title = {Methods of graded rings},
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isbn = {978-3-540-20746-7},
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series = {Lecture notes in mathematics},
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pagetotal = {304},
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number = {1836},
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publisher = {Springer},
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author = {Năstăsescu, Constantin and Oystaeyen, Freddy Van},
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date = {2004},
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keywords = {Associative rings, Graded rings},
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}
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@article{Hochster1972,
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ISSN = {0003486X, 19398980},
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URL = {http://www.jstor.org/stable/1970791},
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author = {Melvin Hochster},
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journal = {Annals of Mathematics},
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number = {2},
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pages = {318--337},
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publisher = {[Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University]},
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title = {Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes},
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urldate = {2026-09-10},
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volume = {96},
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year = {1972}
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}
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@book{Cox2011,
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author = {Cox, David A. and Little, John B. and Schenck, Henry K.},
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title = {Toric Varieties},
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series = {Graduate Studies in Mathematics},
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volume = {124},
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publisher = {American Mathematical Society},
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address = {Providence, RI},
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year = {2011},
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isbn = {978-0-8218-4819-2},
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doi = {10.1090/gsm/124}
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} |