Geodesic
Modules over a~polynomial ring obtained from
Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 423-443

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A construction of Cohen–Macaulay modules over a polynomial ring arising in the study of the Cauchy–Fueter equations is extended from quaternions to arbitrary finite-dimensional associative algebras. It is shown for a certain class of algebras that this construction produces Cohen–Macaulay modules, and this class of algebras cannot be enlarged for a perfect base field. Several properties of this construction are also described. For the class of algebras under consideration several invariants of the resulting modules are calculated. 
@article{SM_2002_193_3_a7,
     author = {O. N. Popov},
     title = {Modules over a~polynomial ring obtained from},
     journal = {Sbornik. Mathematics},
     pages = {423--443},
     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_3_a7/}
}
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O. N. Popov. Modules over a~polynomial ring obtained from. Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 423-443. http://geodesic.mathdoc.fr/item/SM_2002_193_3_a7/