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Research Article

Factorization properties of quotients of polynomial and power series rings by monomial ideals

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Pages 2760-2768 | Received 24 Jul 2023, Accepted 03 Jan 2024, Published online: 27 Jan 2024

References

  • Alan, M. (2012). On finite factorization rings. Commun. Algebra 40:4089–4099. DOI: 10.1080/00927872.2011.602163.
  • Anderson, D. D., Al-Mallah, O. A. (2017). Commutative group rings that are présimplifiable or domainlike. J. Algebra Appl. 16:paper#1750019.
  • Anderson, D. D., Edmonds, R. A. C. (2021). Unique factorization in polynomial rings with zero divisors. J. Algebra Appl. 20(7):paper #2150113. DOI: 10.1142/S0219498821501139.
  • Anderson, D. D., Ganatra, A. (2007). Bounded factorization rings. Commun. Algebra 35:3892–3903. DOI: 10.1080/00927870701509230.
  • Anderson, D. D., Valdes-Leon, S. (1996). Factorization in commutative rings with zero-divisors. Rocky Mount. J. Math. 26:439–480.
  • Anderson, D. D., Valde-Leon, S. (1997). Factorization in commutative rings with zero divisors, II. In: Anderson, D. D., ed. Factorization in Integral Domains. New York: Marcel Dekker, 197–219.
  • Anderson, D. F., Park, J. (1997). Factorization in subrings of K[x] or K[[x]]. In: Anderson, D. D., ed. Factorization in Integral Domains, (1997). New York: Marcel Dekker, 227–241.
  • Becker, T. (1990). Standard bases and some computations in rings of power series. J. Symb. Comput. 10:165–178. DOI: 10.1016/S0747-7171(08)80039-9.
  • Bouvier, A. (1971). Anneaux présimplifiable s et anneaux atomiques. C. R. Acad. Sci. Paris 272:992–994.
  • Brewer, J. W. (1981). Power Series over Commutative Rings. New York: Marcel Dekker.
  • Chang, G. W. (2021). Unique factorization property of non-unique factorization domains. J. Algebra Appl. 20(3):paper #2150038. DOI: 10.1142/S0219498821500389.
  • Chang, G. W., Reinhart, A. (2020). Unique factorization property of non-unique factorization domains II. J Pure Appl. Algebra 224:paper no. 106430. DOI: 10.1016/j.jpaa.2020.106430.
  • Coykendall, J., Trentham, S. (2017). Spontaneous atomicity for polynomial rings with zero divisors. J. Pure Appl. Algebra 221:2192–2197. DOI: 10.1016/j.jpaa.2016.12.002.
  • Ene, V., Herzog, J. (2012). Gröbner Bases in Commutative Algebra. Providence: American Mathematical Society.
  • Fan, Y., Geroldinger, A., Kainrath, F., Tringali, S. (2017). Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules. J. Algebra Appl. 11:paper #1750234.
  • Fan, Y., Tringali, S. (2018). Power monoids: A bridge between factorization theory and arithmetic combinatorics. J. Algebra 512:252–294. DOI: 10.1016/j.jalgebra.2018.07.010.
  • Frei, C., Frisch, S. (2011). Non-unique factorization of polynomials over residue class rings of the integers. Commun. Algebra 39:1482–1490. DOI: 10.1080/00927872.2010.549158.
  • Geroldinger, A., Khadam, M. A. (2022). On the arithmetic of monoids of ideals, Ark. Mat., 60:67–106. DOI: 10.4310/ARKIV.2022.v60.n1.a4.
  • Geroldinger, A., Reinhart, A. (2019). The monotone catenary degree of monoids of ideals. Int. J. Algebra Comput. 29:419–457. DOI: 10.1142/S0218196719500097.
  • Geroldinger, A., Zhong, Q. (2020). Factorization theory in commutative monoids. Semigroup Forum 100:22–51. DOI: 10.1007/s00233-019-10079-0.
  • Gotti, F. (2022). On semigroup algebras with rational exponents. Commun. Algebra 50(1):3–18. DOI: 10.1080/00927872.2021.1949018.
  • Gotti, F., Zafrullah, M. (2023). Integral domains and the IDF property. J. Algebra 614:564–591. DOI: 10.1016/j.jalgebra.2022.08.034.
  • Herzog, J., Hibi, T. (2011). Monomial Ideals. London: Springer-Verlag.
  • Juett, J. R., Medina, A. M. (2022). Finite factorization properties in commutative monoid rings with zero divisors. Commun. Algebra 50(1):392–422. DOI: 10.1080/00927872.2021.1958829.
  • Juett, J. R., Mooney, C. P. (2021). Notions of unique factorization in commutative rings with zero divisors. Houston J. Math. 47(1):1–29.
  • Kim, H. (2001). Factorization in monoid domains. Commun. Algebra 29(5):1853–1869. DOI: 10.1081/AGB-100002153.
  • Nagata, M. (1957). A remark on the unique factorization theorem. J. Math. Soc. Japan 9:143–145. DOI: 10.2969/jmsj/00910143.
  • Nikseresht, A. (2018). Factorization in modules and splitting multiplicatively closed subsets. J. Korean Math. Soc. 55:83–99.
  • Nikseresht, A., Azizi, A. (2017). Factorization with respect to a divisor-closed multiplicative submonioid of a ring. Turk. J. Math. 41:483–499. DOI: 10.3906/mat-1410-42.
  • Nikseresht, A., Azizi, A. (2011). On factorization in modules. Commun. Algebra 39:292–311. DOI: 10.1080/00927870903527535.

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