PowerShell, more efficient way to find duplicate folders

I wrote a little function to scan each folder in $PSModulePath to see if duplicate folder names exist in the various paths in there (as I've found this problem happening quite often in my PowerShell environments!). I use simple logic and I was wondering if some PowerShell gurus maybe have more compact / faster / more efficient ways to achieve a sweep like this (I quite often find that those better at PowerShell seem to have 2-line solutions to something that takes me 15 lines! :-) )?

I'm just taking a path in $PSModulePath and creating an array of the subfolder names there, then looking at the subfolders of the other paths in $PSModulePath and comparing them one by one against the array that I made for the first path, and then repeating for the other paths.

function Find-ModuleDuplicates {
    $hits = ""
    $ModPaths = $env:PSModulePath -Split ";" -replace "\\+$", "" | sort
    foreach ($i in $ModPaths) {
        foreach ($j in $ModPaths) {
            if ($j -notlike "*$i*") {
                $arr_i = (gci $i -Dir).Name
                $arr_j = (gci $j -Dir).Name
                foreach ($x in $arr_j) {
                    if ($arr_i -contains $x) {
                        $hits += "Module '$x' in '$i' has a duplicate`n" 
                    }
                }
            }
        }
    }
    if ($hits -ne "") { echo "" ; echo $hits }
    else { "`nNo duplicate Module folders were found`n" }
}