Question

In "A Classical Introduction to Number theory" by Ireland, Kenneth, The greatest common divisor of a set of numbers is generalized using ideal with the property that (a,b) = (d), If (a,b) = (14,10) then it would seem (d) = 2Z, How then does (14,10) = 2Z, as i can imagine elements in 2Z that would not be in (14,10), like 6,8,12....

Answer 1

Im new to abstract algebra (obviously) and know i am misunderstanding something here, probably about the closure under addition of ideals, i would help if someone could simply write out the first few terms of the set (14,10) as an ideal subset of Z