Semi-chain ring

left (right)

A ring which is a left (right) semi-chain module over itself.

Comments

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.

References

[a1]	C. Faith, "Algebra" , II. Ring theory , Springer (1976) pp. Chapt. 25