โ Scribed by Franz Halter-Koch
No coin nor oath required. For personal study only.
Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids.
Content: Part 1 General ideal theory: monoids and monoid homomorphisms
arithmetic of ideal systems
finitary and noetherian ideal systems
monoids of quotients
comparison and mappings of ideal systems
prime and primary ideals
quotients of primary ideals and primary decompositions
strictly noetherian ideal systems
the intersection theorem and the principal ideal theorem. Part 2 Multiplicative ideal theory: abstract elementary number theory
fractional divisorial ideals
invertible ideals and class groups
arithmetic of invertible and cancellative ideals
integrative closures
valuation monoids and primary monoids
ideal theory of valuation monoids
Prufer and Bezout monoids
essential homomorphisms, GCD-homomorphisms and valuations
Lorenzen monoids
quasi divisor theories
defining systems
Krull monoids and generalizations
(almost) Dedekind and Krull monoids
t-noetherian monoids
approximation theorems
divisorial defining systems and class groups
arithmetical properties of overmonoids
solutions of exercises
a guide to results on special integral domains.
Idealtheorie;Ideals (Algebra);Rings (Algebra)
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"Provides for the first time a concise introduction to general and multiplicative ideal theory, valid for commutative rings and monoids and presented in the language of ideal systems on (commutative) monoids."
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