Talk:Elementary divisors

Not primary ideals

The current article says that elementary divisors are primary, and divide one another. These are however incompatible conditions: consider the cyclic group of order 6: it can be decomposed as product of primary modules over Z by the Chinese remainder theorem, but now the corresponding ideals generated by 2 and 3 do not satisfy any containment. I am going to remove the primary stuff since I think this is the wrong part for the term elementary divisors. Should I be mistaken and "elementary" imply "primary" instead (but no divisibilty) then feel free to make the opposite change (removing the divisibility, but then also the reference to the Smith normal form). Marc van Leeuwen (talk) 14:27, 7 December 2013 (UTC)

Almost! Recall that if n and m are two relatively prime integers, then the product (Z/nZ)×(Z/mZ) is isomorphic to Z/nmZ. 76.74.72.244 (talk) 19:31, 15 March 2023 (UTC)

I forgot to log in when I replied. Snreyes (talk) 19:33, 15 March 2023 (UTC)