http://math.fontein.de/2009/10/02/the-hasse-derivative-part-ii-multivariate-partial-hasse-derivatives/ Focussed on, but not limited to Computational Number Theory Mon, 19 Sep 2011 18:10:41 +0000 hourly 1 http://wordpress.org/?v=3.1 http://math.fontein.de/2009/10/02/the-hasse-derivative-part-ii-multivariate-partial-hasse-derivatives/comment-page-1/#comment-61 Felix Fontein Mon, 05 Oct 2009 17:02:52 +0000 http://math.fontein.de/?p=474#comment-61 Ah, I think this is just a problem with notation. When I wrote, “<i>homomorphism of unitary commutative rings</i>”, I assumed that the homomorphism satisfies $\varphi(1_R) = 1_{R'}$. :-) I think I have to make it a bit more clearly, to make it less confusing... Thanks for the hint! Ah, I think this is just a problem with notation. When I wrote, “homomorphism of unitary commutative rings”, I assumed that the homomorphism satisfies . :-) I think I have to make it a bit more clearly, to make it less confusing… Thanks for the hint!

]]> http://math.fontein.de/2009/10/02/the-hasse-derivative-part-ii-multivariate-partial-hasse-derivatives/comment-page-1/#comment-60 Alexey Maevskiy Mon, 05 Oct 2009 14:19:34 +0000 http://math.fontein.de/?p=474#comment-60 Hello! Thank you for this excellent article! I think it will be useful for many peoples. But I note that in the first proposition it is necessary to add one of the following constraints on the ring homomorphism: $\varphi(1_R)=1_{R'}$ or $\varphi^*(x) = \varphi(1_R)x$. If both requirements does not hold its easy to make a counterexample for situation when proposition is false ($\varphi:Z_{10}\rightarrow Z_{10}$, $\varphi(a)=6a$). Hello! Thank you for this excellent article! I think it will be useful for many peoples.
But I note that in the first proposition it is necessary to add one of the following constraints on the ring homomorphism: or . If both requirements does not hold its easy to make a counterexample for situation when proposition is false (, ).

]]>