Writing commutative diagram in Latex

Question

I am trying to write this in latex but cannot figure out how. I am trying to do the one on the right hand side. I was trying with tikzcd.

Also when I am trying to write the latex for the one on left side, the first down arrow is shifted towards left. Here is my latex code. Below the pic, is the pic of what I am getting with the latex code below.

\[
     \begin{tikzcd}
     K(x) : 0 \arrow{r}  R \arrow{r}{x}  \arrow{d}{y}  & R \arrow{d}{y} \\
     K(x) : 0 \arrow{r}  R \arrow{r}{x} & R
     \end{tikzcd}
\]

Thanks !!!

Answer 1

Basically you are doing it right. You have to shift the lower line by prepending a & and adjusting the arrows to point diagonal. The baseline inside the equation is corrected by “egreg's formula”.

\documentclass{article}
\usepackage{mathtools,tikz-cd}
\begin{document}
\begin{equation*}
  K(x,y):
  \begin{tikzcd}[baseline=\the\dimexpr\fontdimen22\textfont2\relax]
    0 \ar[r] & R \ar[r,"z"]\ar[rd,"y"] & R \ar[r]\ar[rd,"y"]\ar[d,draw=none,"\otimes" description] & 0 \\
    & 0 \ar[r] & R \ar[r,"-z" below] & R \ar[r] & 0 \\
  \end{tikzcd}
\end{equation*}
\end{document}