223 lines
No EOL
7.4 KiB
BibTeX
223 lines
No EOL
7.4 KiB
BibTeX
@article{Shibuta2017,
|
|
title = {Affine semigroup rings are of finite F-representation type},
|
|
volume = {45},
|
|
issn = {0092-7872, 1532-4125},
|
|
url = {https://www.tandfonline.com/doi/full/10.1080/00927872.2017.1313425},
|
|
doi = {10.1080/00927872.2017.1313425},
|
|
pages = {5465--5470},
|
|
number = {12},
|
|
journaltitle = {Communications in Algebra},
|
|
shortjournal = {Communications in Algebra},
|
|
author = {Shibuta, Takafumi},
|
|
urldate = {2026-08-03},
|
|
date = {2017-12-02},
|
|
langid = {english},
|
|
}
|
|
|
|
@article{Hochster1976,
|
|
title = {The purity of the Frobenius and local cohomology},
|
|
journal = {Advances in Mathematics},
|
|
volume = {21},
|
|
number = {2},
|
|
pages = {117-172},
|
|
year = {1976},
|
|
issn = {0001-8708},
|
|
doi = {https://doi.org/10.1016/0001-8708(76)90073-6},
|
|
url = {https://www.sciencedirect.com/science/article/pii/0001870876900736},
|
|
author = {Melvin Hochster and Joel L Roberts}
|
|
}
|
|
|
|
@article{Yasuda2009,
|
|
title = {On monotonicity of F-blowup sequences},
|
|
volume = {53},
|
|
issn = {0019-2082},
|
|
url = {https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-53/issue-1/On-monotonicity-of-F-blowup-sequences/10.1215/ijm/1264170841.full},
|
|
doi = {10.1215/ijm/1264170841},
|
|
number = {1},
|
|
journaltitle = {Illinois Journal of Mathematics},
|
|
shortjournal = {Illinois J. Math.},
|
|
author = {Yasuda, Takehiko},
|
|
urldate = {2026-08-11},
|
|
date = {2009-01-01},
|
|
}
|
|
|
|
@article{Bruns2006,
|
|
title = {On seminormal monoid rings},
|
|
volume = {302},
|
|
rights = {https://www.elsevier.com/tdm/userlicense/1.0/},
|
|
issn = {00218693},
|
|
url = {https://linkinghub.elsevier.com/retrieve/pii/S0021869305006605},
|
|
doi = {10.1016/j.jalgebra.2005.11.012},
|
|
pages = {361--386},
|
|
number = {1},
|
|
journaltitle = {Journal of Algebra},
|
|
shortjournal = {Journal of Algebra},
|
|
author = {Bruns, Winfried and Li, Ping and Römer, Tim},
|
|
urldate = {2026-08-12},
|
|
date = {2006-08},
|
|
langid = {english},
|
|
}
|
|
|
|
@incollection{Bruns2005,
|
|
author = {Bruns, Winfried},
|
|
title = {Conic divisor classes over a normal monoid algebra},
|
|
booktitle = {Commutative Algebra and Algebraic Geometry},
|
|
series = {Contemporary Mathematics},
|
|
volume = {390},
|
|
pages = {63--71},
|
|
publisher = {American Mathematical Society},
|
|
location = {Providence, RI},
|
|
year = {2005},
|
|
}
|
|
|
|
|
|
@incollection{Blickle2013,
|
|
location = {New York, {NY}},
|
|
title = {$p^{-1}$-Linear Maps in Algebra and Geometry},
|
|
isbn = {978-1-4614-5291-1 978-1-4614-5292-8},
|
|
url = {https://link.springer.com/10.1007/978-1-4614-5292-8_5},
|
|
doi = {10.1007/978-1-4614-5292-8_5},
|
|
pages = {123--205},
|
|
booktitle = {Commutative Algebra},
|
|
publisher = {Springer New York},
|
|
author = {Blickle, Manuel and Schwede, Karl},
|
|
editor = {Peeva, Irena},
|
|
urldate = {2026-09-01},
|
|
date = {2013},
|
|
langid = {english},
|
|
}
|
|
|
|
@inbook{Leuschke2012,
|
|
url = {https://doi.org/10.1515/9783110250404.293},
|
|
title = {Non-commutative Crepant Resolutions: Scenes From Categorical Geometry},
|
|
booktitle = {Progress in Commutative Algebra 1},
|
|
booktitle = {Combinatorics and Homology},
|
|
author = {Graham J. Leuschke},
|
|
editor = {Christopher Francisco and Lee C. Klingler and Sean Sather-Wagstaff and Janet C. Vassilev},
|
|
publisher = {De Gruyter},
|
|
address = {Berlin, Boston},
|
|
pages = {293--364},
|
|
doi = {doi:10.1515/9783110250404.293},
|
|
isbn = {9783110250404},
|
|
year = {2012},
|
|
lastchecked = {2026-09-02}
|
|
}
|
|
|
|
@article{Faber2019,
|
|
title = {Non-commutative resolutions of toric varieties},
|
|
journal = {Advances in Mathematics},
|
|
volume = {351},
|
|
pages = {236-274},
|
|
year = {2019},
|
|
issn = {0001-8708},
|
|
doi = {https://doi.org/10.1016/j.aim.2019.04.021},
|
|
url = {https://www.sciencedirect.com/science/article/pii/S0001870819301823},
|
|
author = {Eleonore Faber and Greg Muller and Karen E. Smith},
|
|
keywords = {Toric variety, Non-commutative resolution, Finite global dimension, Non-commutative crepant resolution, Rings of differential operators, Strong F-regularity},
|
|
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.}
|
|
}
|
|
|
|
@book{Dummit2004,
|
|
author = {Dummit, David S. and Foote, Richard M.},
|
|
title = {Abstract Algebra},
|
|
edition = {3},
|
|
publisher = {John Wiley \& Sons},
|
|
location = {Hoboken, NJ},
|
|
year = {2004},
|
|
}
|
|
|
|
@book{Mollin2008,
|
|
location = {Boca Raton},
|
|
edition = {2nd ed},
|
|
title = {Fundamental number theory with applications},
|
|
isbn = {978-1-4200-6659-3},
|
|
series = {Discrete mathematics and its applications},
|
|
pagetotal = {369},
|
|
publisher = {Chapman \& Hall/{CRC}},
|
|
author = {Mollin, Richard A.},
|
|
date = {2008},
|
|
}
|
|
|
|
@book{Nastasescu2004,
|
|
location = {Berlin ; New York},
|
|
title = {Methods of graded rings},
|
|
isbn = {978-3-540-20746-7},
|
|
series = {Lecture notes in mathematics},
|
|
pagetotal = {304},
|
|
number = {1836},
|
|
publisher = {Springer},
|
|
author = {Năstăsescu, Constantin and Oystaeyen, Freddy Van},
|
|
date = {2004},
|
|
keywords = {Associative rings, Graded rings},
|
|
}
|
|
|
|
@article{Hochster1972,
|
|
ISSN = {0003486X, 19398980},
|
|
URL = {http://www.jstor.org/stable/1970791},
|
|
author = {Melvin Hochster},
|
|
journal = {Annals of Mathematics},
|
|
number = {2},
|
|
pages = {318--337},
|
|
publisher = {[Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University]},
|
|
title = {Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes},
|
|
urldate = {2026-09-10},
|
|
volume = {96},
|
|
year = {1972}
|
|
}
|
|
|
|
@book{Cox2011,
|
|
author = {Cox, David A. and Little, John B. and Schenck, Henry K.},
|
|
title = {Toric Varieties},
|
|
series = {Graduate Studies in Mathematics},
|
|
volume = {124},
|
|
publisher = {American Mathematical Society},
|
|
address = {Providence, RI},
|
|
year = {2011},
|
|
isbn = {978-0-8218-4819-2},
|
|
doi = {10.1090/gsm/124}
|
|
}
|
|
|
|
|
|
@article{Geroldinger2025,
|
|
title = {On algebraic properties of power monoids of numerical monoids},
|
|
volume = {265},
|
|
issn = {0021-2172, 1565-8511},
|
|
url = {https://link.springer.com/10.1007/s11856-024-2683-0},
|
|
doi = {10.1007/s11856-024-2683-0},
|
|
pages = {867--900},
|
|
number = {2},
|
|
journaltitle = {Israel Journal of Mathematics},
|
|
shortjournal = {Isr. J. Math.},
|
|
author = {Bienvenu, Pierre-Yves and Geroldinger, Alfred},
|
|
urldate = {2026-09-16},
|
|
date = {2025-02},
|
|
}
|
|
|
|
@book{Rosales2009,
|
|
location = {New York, {NY}},
|
|
title = {Numerical Semigroups},
|
|
volume = {20},
|
|
rights = {https://www.springernature.com/gp/researchers/text-and-data-mining},
|
|
isbn = {978-1-4419-0159-0 978-1-4419-0160-6},
|
|
url = {https://link.springer.com/10.1007/978-1-4419-0160-6},
|
|
doi = {10.1007/978-1-4419-0160-6},
|
|
series = {Developments in Mathematics},
|
|
publisher = {Springer New York},
|
|
author = {Rosales, J.C. and García-Sánchez, P. A.},
|
|
urldate = {2026-09-16},
|
|
date = {2009},
|
|
langid = {english},
|
|
}
|
|
|
|
@book{Bruns1993,
|
|
location = {Cambridge [England] ; New York},
|
|
title = {Cohen-Macaulay rings},
|
|
isbn = {978-0-521-41068-7},
|
|
series = {Cambridge studies in advanced mathematics},
|
|
pagetotal = {403},
|
|
number = {39},
|
|
publisher = {Cambridge University Press},
|
|
author = {Bruns, Winfried and Herzog, Jürgen},
|
|
date = {1993},
|
|
keywords = {Cohen-Macaulay rings},
|
|
} |