On a generalization of I-regularity
Year: 2025
Type: article
Abstract: Let S S be a pomonoid. The projectivity and strong flatness of right S S -posets have been central topics in the homological classification of pomonoids in recent decades. In 2005, Shi et al. introduced I I -regular S S -posets and proved that all its cyclic S S -subposets are projective [ Indecomposable, projective, and flat S-posets , Comm. Algebra 33 (2005), no. 1, 235–251]. Feng subsequently introduced CSF S S -posets, where all its cyclic S S -subposets are strongly flatness [CSF S S -posets and C(P) S S -posets, Master’s thesis, Northwest Normal University, Gansu, 2020]. In this article, we define a new class of strongly (SF)-cyclic S S -posets, which lies strictly between the classes of I I -regular S S -posets and CSF S S -posets. We then provide a homological classification of pomonoids based on this new property of their right (Rees factor) S S -posets.
Source: Open Mathematics
Authors: Husheng Qiao, Leting Feng
Institution: Northwest Normal University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4414311342