Prüfer rings in a certain pullback

References

• Alajbegović, J. H., Osmanagić, E. (1990). Essential valuations of Krull rings with zero divisors. Commun. Algebra. 18: 2007–2020. DOI: 10.1080/00927879008824008.
   Web of Science ®Google Scholar
• Anderson, D. D., Anderson, D. F. (1979). Generalized GCD domains. Comment. Math. Univ. St. Pauli. 28:215–221.
   Google Scholar
• Anderson, D. D., Anderson, D. F., Fontana, M., Zafrullah, M. (2009). On v-domains and star operations. Commun. Algebra. 37:3018–3043. DOI: 10.1080/00927870802502688.
   Web of Science ®Google Scholar
• Anderson, D. D., Kang, B. G. (1989). Pseudo-Dedekind domains and divisorial ideals of R[X]T. J. Algebra. 122:323–336. DOI: 10.1016/0021-8693(89)90219-6.
   Web of Science ®Google Scholar
• Anderson, D. D., Markanda, R. (1985). Unique factorization rings with zero divisors: Corrigendum. Houston J. Math. 11:423–426.
   Web of Science ®Google Scholar
• Anderson, D. D., Mott, J., Zafrullah, M. (1992). Finite character representations for integral domains. Boll. Un. Mat. Ital. B. 6:613–630.
   Google Scholar
• Anderson, D. D., Valdes-Leon, S. (1997). Factorization in commutative rings with zero divisors, II. In: Anderson, D. D., ed. Factorization in Integral Domains. Lecture Notes in Pure and Applied Math., Vol. 189. New York, NY: Marcel Dekker, pp. 197–219.
   Google Scholar
• Anderson, D. D., Winders, M. (2009). Idealization of a module. J. Commut. Algebra. 1:3–56. DOI: 10.1216/JCA-2009-1-1-3.
   Web of Science ®Google Scholar
• Anderson, D. D., Zafrullah, M. (1991). Almost Bézout domains. J. Algebra. 142:285–309. DOI: 10.1016/0021-8693(91)90309-V.
   Web of Science ®Google Scholar
• Badawi, A. (2009). On rings with divided nil ideal: a survey. In: Fontana, M., et al. eds. Commutative Algebra And Its Applications. Berlin: Walter de Gruyter, pp. 21–40.
   Google Scholar
• Bouvier, A. (1982). Le groupe des classes d’un anneau integre. 107eme Congrès National des Sociétés Savantes, Brest, IV:85–92.
   Google Scholar
• Chang, G. W. (2013). Some examples of weakly factorial rings. Korean J. Math. 21:319–323. DOI: 10.11568/kjm.2013.21.3.319.
   Google Scholar
• Chang, G. W., Kang, B. G. (2002). Integral closure of a ring whose regular ideals are finitely generated. J. Algebra. 251:529–537. DOI: 10.1006/jabr.2000.8596.
   Web of Science ®Google Scholar
• Chang, G. W., Kang, B. G. Integral closure of an affine ring. preprint.
   Google Scholar
• Chang, G. W., Oh, J. S. (2022). The monoid of regular elements in commutative rings with zero divisors. Commun. Algebra. 50:1182–1198. DOI: 10.1080/00927872.2021.1979028.
   Web of Science ®Google Scholar
• Costa, D., Mott, J., Zafrullah, M. (1978). The construction D+XDS[X]. J. Algebra. 53:423–439. DOI: 10.1016/0021-8693(78)90289-2.
   Web of Science ®Google Scholar
• Elliott, J. (2019). Rings, Modules, and Closure Operations. Springer Monographs in Mathematics, Cham, Switzerland: Springer.
   Google Scholar
• Geroldinger, A., Halter-Koch F. (2006). Non-Unique Factorizations. Algebraic, Combinatorial and Analytic Theory. Pure and Applied Mathematics, Vol. 278, Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Geroldinger, A., Ramacher, S., Reinhart, A. (2015). On v-Marot Mori rings and C-rings. J. Korean Math. Soc. 52:1–21. DOI: 10.4134/JKMS.2015.52.1.001.
   Web of Science ®Google Scholar
• Gilmer, R. (1972). Multiplicative Ideal Theory, Pure and Applied Mathematics, Vol. 12. New York: Marcel Dekker, Inc.
   Google Scholar
• Glaz, S. (2003). Controlling the zero divisors of a commutative ring. In: Fontana, M., et al. eds. Commutative Ring Theory and Applications. Lecture Notes in Pure and Applied Mathematics, Vol. 231. New York, NY: Marcel Dekker, pp.191–212. DOI: 10.1201/9780203910627-16.
   Google Scholar
• Griffin, M. (1967). Some results on v-multiplication rings. Canad. J. Math. 97:710–722. DOI: 10.4153/CJM-1967-065-8.
   Web of Science ®Google Scholar
• Griffin, M. (1970). Prüfer rings with zero divisors. J. Reine Angew. Math. 239/240:55–67.
   Google Scholar
• Halter-Koch, F. (1993). A characterization of Krull rings with zero divisors. Arch. Math. Brno. 29:119–122.
   Google Scholar
• Halter-Koch, F. (1998). Ideal Systems. Monographs and Textbooks in Pure and Appl. Math., Vol. 211. New York: Marcel Dekker, Inc.
   Google Scholar
• Huckaba, J. (1988). Commutative Rings with Zero Divisors. Monographs and Textbooks in Pure and Applied Mathematics, Vol. 117. New York etc.: Marcel Dekker, Inc.
   Google Scholar
• Jensen, C. U. (1966). Arithmetical rings. Acta Math. Acad. Sci. Hung. 17:115–123. DOI: 10.1007/BF02020446.
   Web of Science ®Google Scholar
• Kang, B. G. (2000). Characterizations of Krull rings with zero divisors. J. Pure Appl. Algebra. 146:283–290. DOI: 10.1016/S0022-4049(98)00100-5.
   Web of Science ®Google Scholar
• Kennedy, R. (1980). Krull rings. Pacific J. Math. 89:131–136. DOI: 10.2140/pjm.1980.89.131.
   Web of Science ®Google Scholar
• Matsuda, R. (1982). On Kennedy’s problems. Comment. Math. Univ. St. Paul. 31:143–145.
   Google Scholar
• Wang, F. G., Kim, H. (2016). Foundations of Commutative Rings and Their Modules. Algebra and Applications, Vol. 22. Singapore: Springer
   Google Scholar
• Yin, H. (2014). Some characterizations of Prüfer v-multiplication rings. J. Math. Res. Appl. 34:295–300.
   Google Scholar
• Zafrullah, M. (1985). A general theory of almost factoriality. Manuscr. Math. 51: 29–62. DOI: 10.1007/BF01168346.
   Web of Science ®Google Scholar
• Zafrullah, M. (1986). On generalized Dedekind domains. Mathematika. 33:285–295. 300011268 DOI: 10.1112/s0025579.
   Web of Science ®Google Scholar
• Zafrullah, M. (1989). Ascending chain condition and star operations. Commun. Algebra. 17:1523–1533. DOI: 10.1080/00927878908823804.
   Web of Science ®Google Scholar