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#The ideal is closed under addition
#The ideal is closed under addition
#The product of an element of the ideal and an element of the initial ring is an element of the ideal
#The product of an element of the ideal and an element of the initial ring is an element of the ideal
== Examples ==
An example is the set of even integers, as a subset of the ring of integers. This is an ideal because:
# 0 is even.
# The sum of two even integers is even.
# The product of an even integer with and any other integer is even.
[[Category:Mathematics]]
[[Category:Mathematics]]