Canonical stretched rings
Nguyen Thi Anh Hang, Do Van Kien, Hoang Le Truong
TL;DR
This paper introduces canonical and sparse stretched rings, providing characterizations and exploring their properties, including a new Gorenstein rings characterization, supported by explicit examples.
Contribution
It defines and characterizes canonical and sparse stretched rings, and offers a novel Gorenstein rings characterization based on maximum sparse ideals.
Findings
Characterization of canonical stretched rings
Introduction of sparse stretched rings and maximum sparse ideals
Gorenstein rings characterized via maximum sparse ideals
Abstract
In this paper, we introduce the concept of canonical stretched rings, sparse stretched rings and maximum sparse ideals. Then we give characterizations of canonical stretched rings and sparse stretched rings; and a characterization of Gorenstein rings in terms of their maximum sparse ideals. Several explicit examples are provided along the paper to illustrate such rings.
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