Example 23.6.2 (Adjoining odd variable). Let $R$ be a ring. Let $(A, \gamma )$ be a strictly graded commutative graded $R$-algebra endowed with a divided power structure as in the definition above. Let $d > 0$ be an odd integer. In this setting we can adjoin a variable $T$ of degree $d$ to $A$. Namely, set

$A\langle T \rangle = A \oplus AT$

with grading given by $A\langle T \rangle _ m = A_ m \oplus A_{m - d}T$. We claim there is a unique divided power structure on $A\langle T \rangle$ compatible with the given divided power structure on $A$. Namely, we set

$\gamma _ n(x + yT) = \gamma _ n(x) + \gamma _{n - 1}(x)yT$

for $x \in A_{even, +}$ and $y \in A_{odd}$.

There are also:

• 2 comment(s) on Section 23.6: Tate resolutions

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 09PH. Beware of the difference between the letter 'O' and the digit '0'.