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A Theory of Hulls for Rings and Modules

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Book cover Ring and Module Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this expository paper, we survey results on the concept of a hull of a ring or a module with respect to a specific class of rings or modules. A hull is a ring or a module which is minimal among essential overrings or essential overmodules from a specific class of rings or modules, respectively. We begin with a brief history highlighting various types of hulls of rings and modules. The general theory of hulls is developed through the investigation of four problems with respect to various classes of rings including the (quasi-) Baer and (FI-) extending classes. In the final section, application to C *-algebras are provided.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana, 70504-1010, USA

    Gary F. Birkenmeier & Gary F. Birkenmeier

  2. Department of Mathematics, Busan National University, Busan, 609-735, South Korea

    Jae Keol Park

  3. Department of Mathematics, Ohio State University, Lima, Ohio, 45804-3576, USA

    S. Tariq Rizvi

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  1. Gary F. Birkenmeier
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  2. Jae Keol Park
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  3. S. Tariq Rizvi
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  4. Gary F. Birkenmeier
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Editors and Affiliations

  1. “Simion Stoilow” Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 010145 Bucharest 1, Romania

    Toma Albu

  2. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA

    Gary F. Birkenmeier

  3. Department of Mathematics, Hacettepe University, Beytepe Çankaya, 06532, Ankara, Turkey

    Ali Erdoğgan  & Adnan Tercan  & 

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Birkenmeier, G.F., Park, J.K., Rizvi, S.T., Birkenmeier, G.F. (2010). A Theory of Hulls for Rings and Modules. In: Albu, T., Birkenmeier, G.F., Erdoğgan, A., Tercan, A. (eds) Ring and Module Theory. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0007-1_2

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