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Putting T-Invertibility to Use

  • Muhammad Zafrullah
Part of the Mathematics and Its Applications book series (MAIA, volume 520)

Abstract

This article gives a survey of how the notion of t-invertibility has, in recent years, been used to develop new concepts that enhance our understanding of the multiplicative structure of commutative integral domains. The concept of t-invertibility arises in the context of star operations. However, in general terms a (fractional) ideal A, of an integral domain D, is t-invertible if there is a finitely generated (fractional) ideal FA and a finitely generated fractional ideal G A -l such that (FG)-1 = D. In a more specialized context the notion of t-invertibility has to do with the t-operation which is one of the so called star operations. There seems to be no book other than Gilmer’s [Gil] that treats star operations purely from a ring theoretic view point. But a lot has changed since Gilmer’s book was published. So I have devoted a part of section 1. to an introduction to star operations, *-invertibility in general, and t-invertibility in particular.

Keywords

Prime Ideal Integral Domain Integral Ideal Principal Ideal Nonzero Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Muhammad Zafrullah
    • 1
  1. 1.Department of Mathematics, SCEN 301The University of ArkansasFayettevilleUSA

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