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).

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 …

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?

Aug 31, 2023 · su (2) vs ZXZ decomposition Ask Question Asked 2 years, 5 months ago Modified 2 years, 5 months ago

Problem: Show that the group given by the presentation $$\\langle x,y,z \\mid xyx^{-1}y^{-2}\\, , \\, yzy^{-1}z^{-2}\\, , \\, zxz^{-1}x^{-2} \\rangle $$ is equivalent ...

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 $XYZ$ rotations to Euler $ZXZ$ rotations Ask Question Asked 13 years, 11 months ago Modified 12 years, 1 month ago

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 ...

Apr 15, 2017 · Note that you never actually used the ring structure or the multiplicative property of a ring homomorphism here, just the Abelian group structure. In other words, since $\mathbb {Z} \times …

Nov 24, 2009 · 2) The free product of Z*Z is not isomorphic to either Z\oplusZ or ZxZ; in fact, Z*Z is nonabelian (as most free products are). 3) SVK is unnecessary for computing pi_1 of the torus.