May 25, 2018 · I find a similar post, which is Describe all ring homomorphisms from Z×Z into Z. I also know the difference between group and ring. But in this case, from ZxZ into Z, I'm so confused. The …

Feb 25, 2020 · ZxZ is the Cartesian product of Z. You'd have met this a long time ago as co-ordinates, (x,y) where both x and y are in Z. f is a function from Z to ZxZ, f (0) for example is (0,5).

we know Z is a PID but there exists no ring isomorphism between ZxZ and Z. So based on this observation can we conclude that ZxZ is not a PID ? I dont think we can because if A and B are …

Convert from fixed axis XYZ X Y Z rotations to Euler ZXZ Z X Z rotations Ask Question Asked 13 years, 9 months ago Modified 11 years, 11 months ago

Apr 1, 2015 · Interesting way to think about it. So, in general, can you never have an isomorphism from a cyclic group to a non-cyclic group of the same order?

On the wikipedia page there is a listing of 12 matrices that can be used to represent a yaw-pitch-roll rotation series (YXZ) as a ZXZ rotation, or an XZX rotation, or an XZY rotation.. 1) Should t...

Jun 3, 2015 · Describe all ring homomorphisms of: a) $\\mathbb{Z}$ into $\\mathbb{Z}$ b) $\\mathbb{Z}$ into $\\mathbb{Z} \\times \\mathbb{Z}$ c) $\\mathbb{Z} \\times \\mathbb{Z ...

Aug 31, 2023 · su (2) vs ZXZ decomposition Ask Question Asked 2 years, 4 months ago Modified 2 years, 4 months ago

Sep 14, 2008 · The function f: ZxZ->Z defined by f (m, n) = 2m - n is proven to be onto, as for every integer y, there exists at least one integer pair (m, n) such that f (m, n) = y. The proof demonstrates …

This proves that y y and z2 z 2 commute. The relation (R2) (R 2) then boils down to z =z2 z = z 2, which gives z = 1 z = 1. Because of the symmetries in the presentation, this proves that the group is trivial. …