# Semi-chain ring

From Encyclopedia of Mathematics

*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 |

**How to Cite This Entry:**

Semi-chain ring. L.A. Skornyakov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Semi-chain_ring&oldid=15827

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098