I would like to know about the relations between Ernst Kummer's invention of complex ideal numbers (and Dedekind's development of them into what is now called ideals) regarding the unique factorization of an integer into primes and the Lasker-Noether Theorem on factorization, which apparently refers to (polynomial) rings. Is the latter just a special case of the former? In which case do they structurally relate to each other? Are there historical connections between them both?
Thanks in advance.