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Matlis’ semi-regularity in trivial ring extensions of integral domains

Volume 150 / 2017

Khalid Adarbeh, Salah Kabbaj Colloquium Mathematicum 150 (2017), 229-241 MSC: Primary 13C10, 13C11, 13E05, 13F05, 13H10; Secondary 16A30, 16A50, 16A52. DOI: 10.4064/cm7032-12-2016 Published online: 4 August 2017

Abstract

This paper contributes to the study of homological aspects of trivial ring extensions (also called Nagata idealizations). Namely, we investigate the transfer of the notion of (Matlis’) semi-regular ring (also known as IF-ring) along with related concepts, such as coherence, to trivial ring extensions of integral domains. All along the paper, we provide new families of examples subject to semi-regularity.

Authors

  • Khalid AdarbehDepartment of Mathematics
    An-Najah National University
    Nablus, Palestine
    e-mail
  • Salah KabbajDepartment of Mathematics and Statistics
    King Fahd University of Petroleum and Minerals
    Dhahran 31261, Saudi Arabia
    e-mail

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