Multiplicative Ideal Theory in Commutative Algebra

Commutative rngs.- Robert Gilmer’s work on semigroup rings.- Numerical semigroup algebras.- Prüfer rings.- Subrings of zero-dimensional rings.- Old problems and new questions around integer-valued polynomials and factorial sequences.- Robert Gilmer’s contributions to the theory of integer-valued polynomials.- Progress on the dimension question for power series rings.- Some research on chains of prime ideals influenced by the writings of Robert Gilmer.- Direct-sum decompositions over one-dimensional Cohen-Macaulay local rings.- An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations.- Generalized Dedekind domains.- Non-unique factorizations: a survey.- Mixed polynomial/power series rings and relatinos among their spectra.- Uppers to zero in polynomial rings.- On the dimension theory of polynomial rings over pullbacks.- Almost Dedekind domains which are not Dedekind.- Integrality properties of polynomial rings and semigroup rings.- Punctually free ideals.- Holomorphy rings of function fields.- The minimal number of generators of an invertible ideal.- About minimal morphisms.- What v-coprimality can do for you.- Some questions for further research.- Robert Gilmer’s published works.- Commutative Algebra at Florida State 1963–1968.