Geodesic
On the Smoothness of Generic Rings for Stably Free Modules
Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 64-70

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We show certain generic rings for stably free modules are smooth. Using the theory of smooth algebras we deduce that these rings are regular when the base ring is regular. Also this enables us to calculate the dimensions of these rings. Gabel used these generic rings to determine the freeness of certain stably free modules. Our results allow a strengthening of his results when restrictions are placed on the type of stably free module—for example orthogonal stably free modules.
DOI : 10.4153/CMB-1982-009-4
Mots-clés : 13C10 
Swift, Robert W. On the Smoothness of Generic Rings for Stably Free Modules. Canadian mathematical bulletin, Tome 25 (1982) no. 1, pp. 64-70. doi: 10.4153/CMB-1982-009-4
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     title = {On the {Smoothness} of {Generic} {Rings} for {Stably} {Free} {Modules}},
     journal = {Canadian mathematical bulletin},
     pages = {64--70},
     year = {1982},
     volume = {25},
     number = {1},
     doi = {10.4153/CMB-1982-009-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-009-4/}
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