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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11457
Title: A note on -domains and -domains
Authors: Kumar, Rahul
Keywords: Mathematics
Δ-domain
λ-domain
Maximal subring
Overring
Valuation domain
Issue Date: 2020
Publisher: The Belgian Mathematical Society
Abstract: Let R be an integral domain. Then R is said to be a λ-domain if the set of all overrings of R is linearly ordered by inclusion. If R1+R2 is an overring of R for each pair of overrings R1,R2 of R, then R is said to be a Δ-domain. We show that if R⊂T is an extension of integral domains such that each proper subring of T containing R is a λ-domain (resp., Δ-domain), then T is a λ-domain (resp., Δ-domain under some conditions). Moreover, the pair (R,T) is a residually algebraic pair. Two new ring theoretic properties, namely λ-property of domains and Δ-property of domains are introduced and studied.
URI: https://projecteuclid.org/journals/bulletin-of-the-belgian-mathematical-society-simon-stevin/volume-27/issue-4/A-note-on-lambda-domains-and-Delta-domains/10.36045/j.bbms.190718.short
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11457
Appears in Collections:Department of Mathematics

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