Its not up to me to define the term Euclidean.   
      
   Am Samstag, 8. Juli 2017 00:33:20 UTC+2 schrieb Richard Fateman:   
   > yes, f  would be the degree in the main variable.   
      
   The full conditions must be satisified (I only   
   copied one, EF1, there might be more):   
      
   (EF1) If a and b are in R and b is nonzero, then there are q and r in R   
   such that a = bq + r and either r = 0 or f(r) < f(b).   
      
   This PDF says:   
      
   "The following definition of a Euclidean (not Euclidian!)   
   domain is very common in textbooks."   
   http://www.math.uconn.edu/~kconrad/blurbs/ringtheory/euclideanrk.pdf   
      
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