Geodesic
Some Examples of Smooth and Regular Rings(1)
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 255-259

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In this note I investigate smoothness and regularity of the ring the ring of integers. These results do not seem to be well known, especially those dealing with regularity. At any rate, several of my colleagues knew that was not smooth, but thought that it might be regular. I was surprised by the number of possibilities that can occur, as well as by the fact that A can be regular but not smooth. As expected the prime 2 plays a special role. Smoothness depends on a, b, c mod 2, and regularity depends on a, b, c mod 4. 
Roberts, Leslie G. Some Examples of Smooth and Regular Rings(1). Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 255-259. doi: 10.4153/CMB-1980-035-1
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     title = {Some {Examples} of {Smooth} and {Regular} {Rings(1)}},
     journal = {Canadian mathematical bulletin},
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     year = {1980},
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     number = {3},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-035-1/}
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