References
- Brodmann, M. P., Sharp, R. Y. (2013). Local Cohomology. An Algebraic Introduction with Geometric Applications (Cambridge Studies in Advanced Mathematics, 136), 2nd ed. Cambridge: Cambridge University Press.
- Bruns, W., Gubeladze, J. (2009). Polytopes, Rings, and K-Theory, Springer Monographs in Mathematics. Dordrecht: Springer.
- Bruns, W., Herzog, J. (1993). Cohen-Macaulay Rings. (Cambridge Studies in Advanced Mathematics, 39). Cambridge: Cambridge University Press.
- Campillo, A., Gimenez, P. (2000). Syzygies of affine toric varieties. J. Algebra. 225(1):142–161. DOI: 10.1006/jabr.1999.8102.
- Danilov, V. I. (1978). The geometry of toric varieties. Russ. Math. Surv. 33(2):97–154. DOI: 10.1070/RM1978v033n02ABEH002305.
- García-Sánchez, P. A., Rosales, J. C. (2002). On Buchsbaum simplicial affine semigroups. Pacific J. Math. 202(2):329–339. DOI: 10.2140/pjm.2002.202.329.
- Goto, S., Suzuki, N., Watanabe, K. (1976). On affine semigroup rings. Jpn. J. Math. 2(1):1–12. DOI: 10.4099/math1924.2.1.
- Herzog, J., Jafari, R., Stamate, D. I. (2020). Ulrich elements in normal simplicial affine semigroups. Pacific J. Math. 309(2):353–380. DOI: 10.2140/pjm.2020.309.353.
- Herzog, J., Mohammadi, F., Page, J. (2019). Measuring the non-Gorenstein locus of Hibi rings and normal affine semigroup rings. J. Algebra. 540:78–99. DOI: 10.1016/j.jalgebra.2019.08.028.
- Hoa, L. T., Trung, N. T. (1986). Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. of Amer. Math. Soc. 298(1):145–167.
- Hoa, L. T., Trung, N. T. (1988). Corrigendum to “Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. of Amer. Math. Soc. 305(2):857.
- Hochster, M. (1972). Rings of invariants of tori, Cohen–Macaulay rings generated by monomials, and polytopes. Ann. Math. 96(2):318–337. DOI: 10.2307/1970791.
- Jafari, R., Yaghmaei, M. (2021). Type and conductor of simplicial affine semigroups. J. Pure Appl. Algebra. 226(3):106844. DOI: 10.1016/j.jpaa.2021.106844.
- Miller, E., Sturmfels, B. (2005). Combinatorial Commutative Algebra, Graduate Texts in Mathematics, 227, Springer-Verlag, New York,
- Rosales, J. C., García-Sánchez, P. A. (1998). On Cohen-Macaulay and Gorenstein simplicial affine semigroups. Proc. Edinburgh Math. Soc. 41(3):517–537. no3DOI: 10.1017/S0013091500019866.
- Stanley, R. (1978). Hilbert functions of graded algebras. Adv. Math. 28(1):57–83. DOI: 10.1016/0001-8708(78)90045-2.