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4 Given a ring $R$ , not necessarily a principal ideal domain, and numbers $a, b in R$ , is the norm of the ideal $langle a, b rangle$ the greatest common divisor of the norms of the numbers $a$ and $b$ ? For example, given that $N(3) = 9$ and $N(1 + sqrt{-5}) = 6$ , is $N(langle 3, 1 + sqrt{-5} rangle) = 3$ ? Or how about $N(3) = 9$ and $N(1 + sqrt{10}) = -9$ , so $N(langle 3, 1 + sqrt{10} rangle) = 3$ also? Related question: Norm of an ideal algebraic-number-theory ideals share | cite | improve this question asked Dec 4 '18 at 22:00 Bob Happ Bob Happ 253 1 2 22

1 I'm reading the N1570 Standard and have a problem to understand the wording of the name space definition. Here is it: 1 If more than one declaration of a particular identifier is visible at any point in a translation unit, the syntactic context disambiguates uses that refer to different entities. Thus, there are separate name spaces for various categories of identifiers, as follows: — label names (disambiguated by the syntax of the label declaration and use); — the tags of structures, unions, and enumerations (disambiguated by following any 32) of the keywords struct, union, or enum); — the members of structures or unions; each structure or union has a separate name space for its members (disambiguated by the type of the expression used to access the member via