New results about normal pairs of rings with zero-divisors

DOI10.1007/s11587-013-0169-1zbMath1301.13008OpenAlexW2079419292MaRDI QIDQ480408

Noômen Jarboui, Mabrouk Ben Nasr

Publication date: 8 December 2014

Published in: Ricerche di Matematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11587-013-0169-1

zbMATH Keywords

integralPrüfer ringring extensiondomainoverringvon Neumann regular ringnormal pair\(P\)-extensiontotal quotient ring

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Integral dependence in commutative rings; going up, going down (13B21) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Other special types of modules and ideals in commutative rings (13C13)

Related Items (15)

Maximal non-prime ideally equal subrings of a commutative ring ⋮ An answer to a question about maximal non-integrally closed subrings ⋮ The Loewy series of an FCP (distributive) ring extension ⋮ Normal pairs of noncommutative rings ⋮ A special chain theorem in the set of intermediate rings ⋮ Maximal non-integrally closed subrings of an integral domain ⋮ Unnamed Item ⋮ The number of intermediate rings in FIP extension of integral domains ⋮ WHEN IS THE INTEGRAL CLOSURE COMPARABLE TO ALL INTERMEDIATE RINGS ⋮ Quasi-Prüfer Extensions of Rings ⋮ Ring extensions with finitely many non-Artinian intermediate rings ⋮ On almost valuation ring pairs ⋮ On the commutative ring extensions with at most two non Prüfer intermediate rings ⋮ Some results about proper overrings of pseudo-valuation domains ⋮ An answer to a problem about the number of overrings

Cites Work

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• A characterization of Prüfer domains in terms of polynomials
• \(\Delta\)-rings
• NORMAL PAIRS WITH ZERO-DIVISORS
• A GENERALIZATION OF PRÜFER'S ASCENT RESULT TO NORMAL PAIRS OF COMPLEMENTED RINGS
• Overrings of Commutative Rings. III: Normal Pairs
• On Inc-Extensions and Polynomials with Unit Content
• Coherent Overrings
• Lying-Over Pairs of Commutative Rings
• Some Properties of Integral Closure
• Prüfer rings with zero divisors.

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