DSpace logo

Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11461
Title: A question about maximal non ϕ -chained subrings
Authors: Kumar, Rahul
Keywords: Mathematics
Maximal non ϕ-chained ring
Integrally closed rings
ϕ-Pr\"ufer ring
Issue Date: Jan-2023
Publisher: The Korean Mathematical Society.
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 \cite{rahul} 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://ckms.kms.or.kr/journal/view.html?doi=10.4134/CKMS.c210272
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11461
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.