abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

, particularly ring theory, maximal common divisors are an abstraction of the

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

concept of

greatest common divisor In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers , , the greatest co ...

(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.

d\in H

is a maximal common divisor of a subset,

B\subset H

, if the following criteria are met: #

d, b

for all

b\in B

# Suppose

c\in H

d, c

and

c, b

for all

b\in B

. Then

c \simeq d

References

Abstract algebra {{abstract-algebra-stub