DSpace logo

Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17444
Title: A question about maximal non φ-chained subrings
Authors: Kumar, Rahul
Keywords: Mathematics
Maximal non ${\phi}$-chained ring
Integrally closed ring
${\phi}$-Prufer ring
Issue Date: 2023
Publisher: Korea Science
Abstract: Let 𝓗0 be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗0. This generalization was introduced in [20] where the authors proved that if R ∈ 𝓗0 is an integrally closed ring with finite Krull dimension, then R is a maximal non φ-chained subring of T(R) if and only if R is not local and |[R, T(R)]| = dim(R) + 3. This motivates us to investigate the other natural numbers n for which R is a maximal non φ-chained subring of some overring S. The existence of such an overring S of R is shown for 3 ≤ n ≤ 6, and no such overring exists for n = 7.
URI: https://koreascience.kr/article/JAKO202311857437671.page
http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17444
Appears in Collections:Department of Mathematics

Files in This Item:
There are no files associated with this item.


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.