the generalized principal ideal theorem is one of the cornerstones of dimension theory for noetherian rings. for an r-module m, we identify certain submodules of m that play a role analogous to that of prime ideals in the ring r. using this definition, we extend the generalized principal ideal theorem to modules.

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

A four port network adder-subtractor module, for surface plasmon polariton (SPP) waves based on a ring resonator filter is proposed. The functionality of module is achieved by the phase difference manipulation of guided SPPs through different arms connected to the ring resonator. The module is designed using the concepts of a basic two-port device proposed in this paper. It is shown that two po...