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Putting T-Invertibility to Use

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Non-Noetherian Commutative Ring Theory

Part of the book series: Mathematics and Its Applications ((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 F ⊆ A 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.

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  1. Department of Mathematics, SCEN 301, The University of Arkansas, Fayetteville, AR, 72701, USA

    Muhammad Zafrullah

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  1. Muhammad Zafrullah
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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, Texas, USA

    Scott T. Chapman

  2. Department of Mathematics, The University of Connecticut, Storrs, Connecticut, USA

    Sarah Glaz

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Zafrullah, M. (2000). Putting T-Invertibility to Use. In: Chapman, S.T., Glaz, S. (eds) Non-Noetherian Commutative Ring Theory. Mathematics and Its Applications, vol 520. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3180-4_20

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  • DOI: https://doi.org/10.1007/978-1-4757-3180-4_20

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