In
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ' ...
, particularly
ring theory, maximal common divisors are an abstraction of the
number theory concept of
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.
is a maximal common divisor of a subset,
, if the following criteria are met:
#
for all
# Suppose
,
and
for all
. Then
.
References
Abstract algebra
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