References
- D. D. Anderson, A. G. Agargun, and S. Valdes-Leon, Factorization in commutative rings with zero divisors. III, Rocky Mountain J. Math. 31 (2001), no. 1, 1-21. https://doi.org/10.1216/rmjm/1008959664
- D. D. Anderson and S. Chun, Irreducible elements in commutative rings with zerodivisors, Houston J. Math. 37 (2011), no. 3, 741-744.
- D. D. Anderson and R. Markanda, Unique factorization rings with zero divisors, Houston J. Math. 11 (1985), no. 1, 15-30.
- D. D. Anderson and R. Markanda, Corrigendum: "Unique factorization rings with zero divisors", Houston J. Math. 11 (1985), no. 3, 423-426.
- D. D. Anderson and S. Valdes-Leon, Factorization in commutative rings with zero divisors, Rocky Mountain J. Math. 26 (1996), no. 2, 439-480. https://doi.org/10.1216/rmjm/1181072068
- D. D. Anderson and S. Valdes-Leon, Factorization in commutative rings with zero divisors. II, Factorization in integral domains (Iowa City, IA, 1996), 197-219, Lecture Notes in Pure and Appl. Math., 189, Dekker, New York, 1997.
- G. W. Chang, Characterizations of a Krull ring R[X], Bull. Korean Math. Soc. 38 (2001), no. 3, 543-549.
- G. W. Chang, Eakin-Nagata theorem for commutative rings whose regular ideals are finitely generated, Korean J. Math. 18 (2010), 271-275.
- G. W. Chang and B. G. Kang, Integral closure of a ring whose regular ideals are finitely generated, J. Algebra 251 (2002), no. 2, 529-537. https://doi.org/10.1006/jabr.2000.8596
- G. W. Chang and D. Smertnig, Factorization in the self-idealization of a PID, Boll. Unione Mat. Ital. (9) 6 (2013), no. 2, 363-377.
- S. Chun, D. D. Anderson, and S. Valdez-Leon, Reduced factorizations in commutative rings with zero divisors, Comm. Algebra 39 (2011), no. 5, 1583-1594. https://doi.org/10.1080/00927871003666397
- A. Foroutan and A. Geroldinger, Monotone chains of factorizations in C-monoids, Arithmetical properties of commutative rings and monoids, 99-113, Lect. Notes Pure Appl. Math., 241, Chapman & Hall/CRC, Boca Raton, FL, 2005.
- A. Foroutan and W. Hassler, Factorization of powers in C-monoids, J. Algebra 304 (2006), no. 2, 755-781. https://doi.org/10.1016/j.jalgebra.2005.11.006
- R. M. Fossum, The Divisor Class Group of a Krull Domain, Springer, 1973.
- C. Frei and S. Frisch, Non-unique factorization of polynomials over residue class rings of the integers, Comm. Algebra 39 (2011), no. 4, 1482-1490. https://doi.org/10.1080/00927872.2010.549158
- W. Gao and A. Geroldinger, On products of k atoms, Monatsh. Math. 156 (2009), no. 2, 141-157. https://doi.org/10.1007/s00605-008-0547-z
- A. Geroldinger, Additive group theory and non-unique factorizations, Combinatorial number theory and additive group theory, 1-86, Adv. Courses Math. CRM Barcelona, Birkhuser Verlag, Basel, 2009.
- A. Geroldinger and F. Halter-Koch, Non-Unique Factorizations, Algebraic, Combina-torial and Analytic Theory, Pure and Applied Mathematics, vol. 278, Chapman & Hall/CRC, 2006.
- S. Glaz, Controlling the zero divisors of a commutative ring, Commutative ring theory and applications (Fez, 2001), 191-212, Lecture Notes in Pure and Appl. Math., 231, Dekker, New York, 2003.
- F. Halter-Koch, A characterization of Krull rings with zero divisors, Arch. Math. (Brno) 29 (1993), no. 1-2, 119-122.
- F. Halter-Koch, Ideal Systems, Monographs and Textbooks in Pure and Applied Mathematics, 211. Marcel Dekker, Inc., New York, 1998.
- F. Halter-Koch, Weak module systems and applications: a multiplicative theory of integral elements and the Marot property, Commutative ring theory and applications (Fez, 2001), 213-231, Lecture Notes in Pure and Appl. Math., 231, Dekker, New York, 2003.
- F. Halter-Koch, Multiplicative ideal theory in the context of commutative monoids, Commuta-tive Algebra: Noetherian and Non-Noetherian Perspectives (M. Fontana, S.-E. Kabbaj, B. Olberding, and I. Swanson, eds.), pp. 203-231, Springer, 2011.
- J. A. Huckaba, Commutative rings with zero divisors, Pure and Applied Mathematics, vol. 117, Marcel Dekker, 1988.
- B. G. Kang, A characterizations of Krull rings with zero divisors, J. Pure Appl. Algebra 72 (1991), no. 1, 33-38. https://doi.org/10.1016/0022-4049(91)90127-N
- B. G. Kang, Integral closure of rings with zero-divisors, J. Algebra 162 (1993), no. 2, 317-323. https://doi.org/10.1006/jabr.1993.1256
- B. G. Kang, Characterizations of Krull rings with zero divisors, J. Pure Appl. Algebra 146 (2000), no. 3, 283-290. https://doi.org/10.1016/S0022-4049(98)00100-5
- R. E. Kennedy, Krull rings, Pacific J. Math. 89 (1980), no. 1, 131-136. https://doi.org/10.2140/pjm.1980.89.131
- T. G. Lucas, The Mori property in rings with zero divisors, Rings, modules, algebras, and abelian groups, 379-400, Lecture Notes in Pure and Appl. Math., 236, Dekker, New York, 2004.
- T. G. Lucas, Krull rings, Prufer v-multiplication rings and the ring of finite fractions, Rocky Mountain J. Math. 35 (2005), no. 4, 1251-1325. https://doi.org/10.1216/rmjm/1181069687
- T. G. Lucas, The Mori property in rings with zero divisors. II, Rocky Mountain J. Math. 37 (2007), no. 4, 1195-1228. https://doi.org/10.1216/rmjm/1187453107
- C. P. Mooney, Generalized factorization in commutative rings with zero-divisors, Houston J. Math., to appear.
- E. Osmanagic, On an approximation theorem for Krull rings with zero divisors, Comm. Algebra 27 (1999), no. 8, 3647-3657. https://doi.org/10.1080/00927879908826653
- D. Portelli and W. Spangher, Krull rings with zero divisors, Comm. Algebra 16 (1983), no. 16, 1817-1851.
- A. Reinhart, On integral domains that are C-monoids, Houston J. Math. 39 (2013), no. 4, 1095-1116.
- W. A. Schmid, Characterization of class groups of Krull monoids via their systems of sets of lengths: a status report, Number Theory and Applications: Proceedings of the International Conferences on Number Theory and Cryptography (S. D. Adhikari and B. Ramakrishnan, eds.), pp. 189-212, Hindustan Book Agency, 2009.
Cited by
- Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules 2016, https://doi.org/10.1142/S0219498817502346
- Arithmetic of seminormal weakly Krull monoids and domains vol.444, 2015, https://doi.org/10.1016/j.jalgebra.2015.07.026
- The Monotone Catenary Degree of Monoids of Ideals pp.1793-6500, 2019, https://doi.org/10.1142/S0218196719500097
- A characterization of seminormal C-monoids pp.2198-2759, 2019, https://doi.org/10.1007/s40574-019-00194-9