# Vector ring

From Encyclopedia of Mathematics

A partially ordered ring (cf. Partially ordered set) which is a subdirect sum of totally ordered rings (cf. Totally ordered set). Each element of a vector ring is a vector

with coordinates in , and if and only if each . If the partial order of is an intersection of total orders, will be a vector ring, and itself, provided with various linear extensions of its partial order, may be taken as .

#### References

[1] | L. Fuchs, "Partially ordered algebraic systems" , Pergamon (1963) |

**How to Cite This Entry:**

Vector ring.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Vector_ring&oldid=16239

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article