@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}
}