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