We prove a generalization of Luh's result without using Dirichlet's Theorem. We then use Theorem 1 to show that the J-subrings of a periodic ring form a lattice with respect to join and intersection (the join of two subrings is the smallest subring containing both of them). After noting that every J-ring has nonzero characteristic, we determine for which positive integers n and m there exist J-rings of period n and characteristic m. This generalizes a problem posed by G. Wene.
© 1976 Mathematical Association of America
Chinburg, Ted and Melvin Henriksen. "Multiplicatively periodic rings." The American Mathematical Monthly 83.7 (1976): 547-549.