This paper treats the structure of those lattice-ordered rings which are subdirect sums of totally ordered rings -- the f-rings of Birkhoff and Pierce . Broadly, it splits into two parts, concerned respectively with identical equations and with ideal structure; but there is an important overlap at the beginning.
© 1962 Mathematical Sciences Publishers
Henriksen, Melvin, and J. R. Isbell. "Lattice-ordered rings and function rings." Pacific Journal of Mathematics 12.2 (1962): 533-565.