We characterize G-GCD domains and PVMDs as Kaplansky-type theorems. We also give the unified ideal-wise version of a Kaplansky-type theorem. As a consequence, we recover well-known characterization of UFDs, π-domains, and Krull domains. Finally, we c...
We characterize G-GCD domains and PVMDs as Kaplansky-type theorems. We also give the unified ideal-wise version of a Kaplansky-type theorem. As a consequence, we recover well-known characterization of UFDs, π-domains, and Krull domains. Finally, we characterize PVMDs as a Nagata-type theorem.