"Number ring" has a specific meaning [0]. I am not sure if it is equivalent to the integers adjoined with some element though. >In fact the usual integer numbe

"Number ring" has a specific meaning [0]. I am not sure if it is equivalent to the integers adjoined with some element though. >In fact the usual integer numbers we use form a ring too. Depending on definitions, the integers can be viewed as the ring of even numbers adjoined with the element 1. This does require that we do not define rings to necessarily contain 1. In my experience this definition is is becoming more of a historical footnote though. There is also a natural generalization of adjoining multiple elements to the natural numbers (which still results in a ring) In this case, the natural numbers would just be a special case of adjoining 0 elements. The ring of real numbers, in contrast, cannot be constructed by adjoining any finite set of elements to the integers. The ring of integers mod n is also a ring, but does not contain the integers as a subring (and therefore cannot be thought of as the integers adjoined with any set (finite or infinite) of elements). The polynomials with coeficients mod n form a non-finite ring which does not contain the integers. I suspect the point that the author was attempting to make was just that Z[√5] formed a type of structure that mathematicians are familiar with. [0] http://mathworld.wolfram.com/NumberRing.html http://mathworld.wolfram.com/NumberRing.html