Rings in which every regular ideal is finitely generated
Mohamed Chhiti\,^1 and Salah Eddine Mahdou\,^2
\,^1 Laboratory of Modelling and Mathematical Structures,
Faculty of Economics and Social Sciences of Fez, University S.M. Ben Abdellah Fez, Morocco
\,^2 Laboratory of Modelling and Mathematical Structures,
Faculty of Sciences and Technology of Fez, University S.M. Ben Abdellah Fez, Morocco.
Pages 218–225 | Received 15 February 2023, Accepted 28 July 2023, Published 11 December 2023
Abstract
In this paper, we introduce a weak version of Noetherianity that we call regular Noetherian property. A ring is called regular Noetherian, if every regular ideal is finitely generated. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated duplication of a ring along an ideal. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.
Keywords: UN-ring, strongly UN-ring, pullbacks, trivial ring extension, amalgamation.
MSC numbers: 13A15, 13A18, 13F05, 13G05, 13C20.
Downloads: Full-text PDF