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A Unified Approach to Generalizing π‐Extending and π‐Baer Rings

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  • Yeliz Kara

Abstract

This paper introduces and examines the right essentially π‐Baer ring property, which serves as a new extension of the π‐extending and π‐Baer ring conditions. The initial phase of the study involves the development of several foundational results. The subsequent phase of the study involves the exploration of the transfer of the right essentially π‐Baer condition between a ring R and its various ring extensions. The paper provides a characterization of the right essentially π‐Baer generalized triangular matrix rings, as well as n × n upper triangular matrix rings of R and a specific type of trivial extension of R. The findings are illustrated by means of several examples.

Suggested Citation

  • Yeliz Kara, 2025. "A Unified Approach to Generalizing π‐Extending and π‐Baer Rings," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:5579681
    DOI: 10.1155/jom/5579681
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    References listed on IDEAS

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    1. Gary F. Birkenmeier & Jae Keol Park & S Tariq Rizvi, 2013. "Extensions of Rings and Modules," Springer Books, Springer, edition 127, number 978-0-387-92716-9, January.
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