# Maximal common divisor

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In [abstract algebra](/source/Abstract_algebra), particularly [ring theory](/source/Ring_theory), **maximal common divisors** are an abstraction of the [number theory](/source/Number_theory) concept of [greatest common divisor](/source/Greatest_common_divisor) (GCD). This definition is slightly more general than GCDs, and may exist in rings in which GCDs do not. Halter-Koch (1998) provides the following definition.[1]

d\in H is a maximal common divisor of a subset, B\subset H , if the following criteria are met:

1. d|b for all b\in B
1. Suppose c\in H, d|c and c|b for all b\in B. Then c \simeq d.

## References

1. Halter-Koch, Franz (1998). *Ideal systems*. Marcel Dekker. ISBN 0-8247-0186-0.

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