Communications in Algebra · 2003 · 51 citations · 2 references
Natural SciencesMathematicsAlgebraAbstract AlgebraAlgebraic GeometryAlgebraic StructuresArithmetic GeometryCommutative AlgebraAlgebraic ExtensionsDiscrete Valuation RingsField ExtensionsIdeal TheoryIntegral ClosureRing-theoretic Formulations
Abstract We provide an axiomatic concept of Kronecker function rings and apply it to associate a Kronecker function ring to any integral domain D and any ideal system (star operation) on D. We investigate its behavior in algebraic field extensions and its connection with the defining valuation domains.
2
P. M. Cohn · Bulletin of the London Mathematical Society · 1974 · 1.1K citations
Rings with a theory of greatest common divisors
Friedemann Lucius · manuscripta mathematica · 1998 · 11 citations