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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


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.


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

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