@book{serre2000local, title={Local Algebra}, author={Serre, Jean-Pierre}, translator={Chin, CheeWhye}, series={Springer Monographs in Mathematics}, year={2000}, publisher={Springer Berlin Heidelberg} } @book{roberts1998multiplicities, title={Multiplicities and Chern Classes in Local Algebra}, author={Roberts, Paul C.}, series={Cambridge Tracts in Mathematics}, year={1998}, publisher={Cambridge University Press} } @book{eisenbud2004commutative, title={Commutative Algebra}, subtile={with a View Toward Algebraic Geometry}, author={Eisenbud, David}, series={Graduate Texts in Mathematics}, year={2004}, publisher={Springer New York} } @unpublished{ash2003acourse, author = {Ash, Robert B.}, title = {A Course In Commutative Algebra}, year = 2003, url = {http://www.math.uiuc.edu/~r-ash/ComAlg.html}, urldate = {2017-08-16} } @book{cartan1956homological, title={Homological Algebra}, author={Cartan, Henri and Eilenberg, Samuel}, series={Princeton Mathematical Series}, year={1956}, publisher={Princeton University Press} } @book{bourbaki2006algebre, title={Algèbre commutative}, subtitle={Chapitres 1 à 4}, author={Bourbaki, Nicolas}, year={2006}, publisher={Springer Berlin Heidelberg} } @article{EGA, title={Éléments de géométrie algébrique}, author={Grothendieck, Alexander and Dieudonné, Jean}, year={1961--1967}, volume={4 (Chapter 0, 1–7, and I, 1–10), 8 (II, 1–8), 11 (Chapter 0, 8–13, and III, 1–5), 17 (III, 6–7), 20 (Chapter 0, 14– 23, and IV, 1), 24 (IV, 2–7), 28 (IV, 8–15), 32 ((IV, 16–21)}, journal={Publications Mathématiques de l'Institut des Hautes Études Scientifiques} } @article{bardavid11aneffective, title={An Effective Description of {$k[[X]] \otimes_k k[[Y]]$}}, author={Bardavid, Colas}, year={2011}, volume={5}, number={18}, pages={873 - 882}, journal={International Journal of Algebra}, } @article{auslander59unique, title={Unique factorization in regular local rings}, author={Auslander, Maurice and Buchsbaum, David Alvin}, year={1959}, volume={45}, pages={733 – 734}, journal={Proceedings of the National Academy of Sciences of the United States of America}, } @book{kaplansky1974commutative, title={Commutative Rings}, author={Kaplansky, Irving}, series={Chicago Lectures in Mathematics}, year={1974}, publisher={University of Chicago Press} } @article{cohen46onthestructure, title={On the structure and ideal theory of complete local rings}, author={Cohen, Irvin Sol}, year={1946}, volume={59}, pages={54 - 106}, journal={Transactions of the American Mathematical Society}, }