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UMT-domains: A Survey

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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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