Dunn.test in R: are adjusted p-values corrected for number of comparisons? I've performed a post-hoc Dunn's test with Sidak adjustment using the dunn.test code for R.  There are three groups in my comparison and I understand from the R help files that the lower number in the output is the adjusted p-value which I use to compare to alpha (0.05).  
My question is: do I divide alpha by three (since I've three comparisons), or does the adjusted p-value generated by R factor in that I have three comparisons and I simply compare the value with alpha?
Thanks for any help (including pointing me to another discussion).  Have googled in vain.

EDIT: I first performed a Kruskal-Wallis test and a signficanct difference in the groupings was identified.  Also I am very new to R and have read to the best of my ability before posting (am not a statistician).  I do understand from the dunn.test manual that the output from holm adjustment and others mark rejection with a asterisk.  It is interpretation of the Sidak output I'm confused about
 A: Author of dunn.test here. As per the help file for dunn.test under the sidak option for the method argument:

the FWER is controlled using Šidák's (1967) adjustment, and adjusted p-values = max(1, 1 - (1 - p)^m).

So, Yes. dunn.test corrects p-values for multiple comparisons given the argument to method. For the Šidák option, you would reject each null hypothesis if $p\le \alpha/2$ (i.e. dunn.test report one-sided p-values).
Also from the help file:

method adjusts the p-value for multiple comparisons using the Bonferroni, Šidák, Holm, Holm-Šidák, Hochberg, Benjamini-Hochberg, or Benjamini-Yekutieli adjustment (see Details). The default is no adjustment for multiple comparisons.

For the stepwise multiple comparisons adjustment methods, because rejection depends both on adjusted p-values (sometimes called q-values) and the ordering of unadjusted p-values, rejection decisions for a specified level of $\alpha$ are starred in the output.
The advantage of not starring output for the static results is that adjusted p-values can be interpreted by the reader according to their own preference for $\alpha$.
