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- Title
ON MAXIMAL NON-ACCP SUBRINGS.
- Authors
AYACHE, AHMED; DOBBS, DAVID E.; ECHI, OTHMAN; Facchini, A.
- Abstract
A domain R is a maximal non-ACCP subring of its quotient field if and only if R is either a two-dimensional valuation domain with a DVR overring or a one-dimensional nondiscrete valuation domain. If R ⊂ S is a minimal ring extension and S is a domain, then (R,S) is a residually algebraic pair. If S is a domain but not a field, a maximal non-ACCP subring extension R ⊂ S is a minimal ring extension if (R,S) is a residually algebraic pair and R is quasilocal. Results with a similar flavor are given for domains R ⊂ S sharing a nonzero ideal, with applications to rings R of the form A + XB[X] or A + XB[[X]]. If R ⊂ S is a minimal ring extension such that R is a domain and S is not (R-algebra isomorphic to) an overring of R, then R satisfies ACCP if and only if S satisfies ACCP.
- Subjects
RING theory; RING extensions (Algebra); INTEGRAL domains; KRULL rings; ALGEBRAIC functions; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2007, Vol 6, Issue 5, p873
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498807002545