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Vector ring

From Encyclopedia of Mathematics
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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