Regarding Z*(SqrtD) = {x + y SqrtD; integer x,y,D>=0}... 1. What's best to call the components x & y of an element? For D<0 it'd be "real" & "imaginary" parts, but these elements are always purely real numbers. Calling x the "integer part" is confusing with the result of entier/floor (eg the "integer part" of 1+Sqrt2 might mean 1 or 2)... I'm tempted to call them the "rational" & "quadratic" parts (though strictly speaking x here is a "rational integer"<;-). 2. What's best to call the whole algebraic structure? Surely not a "quadratic field"--it lacks both additive and multiplicative inverses? Perhaps a "quadratic (commutative) semiring"? Is there good conventional nomenclature for this? If not, would any of the above work, or could you suggest something better? Thanks!