Matlis’ semi-regularity in trivial ring extensions of integral domains
Tom 150 / 2017
Colloquium Mathematicum 150 (2017), 229-241 MSC: Primary 13C10, 13C11, 13E05, 13F05, 13H10; Secondary 16A30, 16A50, 16A52. DOI: 10.4064/cm7032-12-2016 Opublikowany 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.