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- Title
NORMAL PAIRS WITH ZERO-DIVISORS.
- Authors
DOBBS, DAVID E.; SHAPIRO, JAY; Facchini, A.
- Abstract
Results of Davis on normal pairs (R, T) of domains are generalized to (commutative) rings with nontrivial zero-divisors, particularly complemented rings. For instance, if T is a ring extension of an almost quasilocal complemented ring R, then (R, T) is a normal pair if and only if there is a prime ideal P of R such that T = R[P], R/P is a valuation domain and PT = P. Examples include sufficient conditions for the "normal pair" property to be stable under formation of infinite products and ⋈ constructions.
- Subjects
RING theory; SMALL divisors; ASSOCIATIVE rings; VALUATION theory; QUOTIENT rings; MATHEMATICAL analysis; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2011, Vol 10, Issue 2, p335
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498811004628