UMT-domains: A Survey

  • Gyu Whan ChangEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 321)


Let D be an integral domain, X be an indeterminate over D, and D[X] be the polynomial ring over D. A nonzero prime ideal Q of D[X] is called an upper to zero in D[X] if \(Q \cap D = (0)\). We say that D is a UMT-domain if each upper to zero in D[X] is a maximal t-ideal of D[X]. The notion of UMT-domains was introduced by Houston and Zafrullah in 1989. In this paper, we survey the results on UMT-domains with focus on uppers to zero, Nagata rings, graded integral domains, and constructions of new UMT-domains.


t-operation Upper to zero UMT-domain Nagata ring Graded integral domain 



This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2017R1D1A1B06029867).


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Authors and Affiliations

  1. 1.Department of Mathematics EducationIncheon National UniversityIncheonKorea

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