Is Wikipidia wrong about Schnorr Signatures? Wikipidia says Schnorr signature generation is defined like this:

Y = x * G //this is the key we are trying to provide a signature for
k = random scalar
r = k * G
e = Hash_to_scalar(r || message)
s = k - xe
signature = (s, e)


This seems correct, but then to verify it's defined as:

r = s * G * e * Y
e = Hash_to_scalar(r || message)


Shouldn't it be:

r = s * G + e * Y
e = Hash_to_scalar(r || message)


because:

r = k - xe * G + ex * G == k * G; //this works
r = k - xe * G * ex * G != k * G; //this doesnt work


Or have I made a silly mistake somewhere?
The equation in Wikipedia is r = s*G + e*Y, and not r = s*G * e*Y

Thus, r = s*G + e*Y = (k - xe)*G + e*(x*G) = k*G - xe*G + xe*G = k*G