Charles W. Adams was elected colonel of the 23rd Arkansas Infantry on April 25, 1862, and resigned when his regiment was field-consolidated with the 12th and 14th Arkansas Regiments at Saltillo, Mississippi, on September 10, 1862. The 23rd Arkansas was east of the Mississippi River when the battle of Prairie Grove took place on December 7, 1862.
The regiment known as Adams' Arkansas Regiment, the one which fought at Prairie Grove and was later disbanded, was one of three regiments which were initially known as the 1st, 2nd and 3rd Regiments, Northwest Division (Adams' being the 3rd Regiment).
These regiments were authorized by the State Military Board as the 34th, 35th and 36th Arkansas Infantry (Adams' being the 36th Arkansas), but these designations were not used before Prairie Grove. The 35th Arkansas was known then as Rector's 1st Arkansas, the 34th Arkansas as Brooks' 2nd Arkansas, and the 36th Arkansas as Adams' 3rd Arkansas.
The 34th and 35th Arkansas finally took up these designations after Prairie Grove (though the 35th was later resignated as the 22nd Arkansas). Adams' regiment was disbanded after Prairie Grove and its designation of 36th Arkansas was given to the 28th Arkansas. So, while the records of the State Military Board refer to Adams' regiment as the (first) 36th Arkansas, this designation was never officially used.
I hope you can make some sense out of this jumble. This was not an easy puzzle to work out, let me tell you -- and it's just about as hard to explain as it was to research!
One of the legacies of this confusion is that some people still insist today that Adams' 3rd Arkansas (Northwest Division) was really Manning's 3rd Arkansas (Army of Northern Virginia), which commuted back to Arkansas for the Prairie Grove fight. In fact, when the battle of Prairie Grove took place, Manning's "real" 3rd Arkansas was digging in on the heights south of Fredericksburg, Virginia, getting ready to welcome the Union Army of the Potomac.