Such a ring is also called right serial (respectively, left serial). A serial ring is one which is both left and right serial. An example of a serial ring is the ring of formal power series in one variable over a field.
|[a1]||C. Faith, "Algebra" , II. Ring theory , Springer (1976) pp. Chapt. 25|
Semi-chain ring. L.A. Skornyakov (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-chain_ring&oldid=15827