Clifford extensions. (English) Zbl 1344.16010
Summary: Formulating the construction of Clifford algebras, we introduce the notion of Clifford extensions and show that Clifford extensions are Frobenius extensions. Consequently, Clifford extensions of Auslander-Gorenstein rings are Auslander-Gorenstein rings.
MSC:
16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
16S35 | Twisted and skew group rings, crossed products |
15A66 | Clifford algebras, spinors |
16E10 | Homological dimension in associative algebras |
References:
[1] | DOI: 10.1007/s10468-007-9065-2 · Zbl 1177.16015 · doi:10.1007/s10468-007-9065-2 |
[2] | DOI: 10.1007/BF01243916 · Zbl 0763.14001 · doi:10.1007/BF01243916 |
[3] | Björk J.-E., Rings of Differential Operators (1979) |
[4] | Björk, J.E. (1989). The Auslander condition on noetherian rings. In:Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année (Paris, 1987/1988).Lecture Notes in Math., Vol. 1404. Berlin: Springer, pp. 137–173. · doi:10.1007/BFb0084075 |
[5] | Fossum R. M., Trivial Extensions of Abelian Categories (1976) |
[6] | DOI: 10.1017/CBO9780511972997 · doi:10.1017/CBO9780511972997 |
[7] | DOI: 10.1142/S0219498815501005 · Zbl 1332.16033 · doi:10.1142/S0219498815501005 |
[8] | Karpilovsky G., The Algebraic Structure of Crossed Products (1987) · Zbl 0614.16001 |
[9] | Nakayama T., Nagoya Math. J 17 pp 89– (1960) |
[10] | Nakayama T., Nagoya Math. J 19 pp 127– (1961) |
[11] | DOI: 10.1007/s002220050065 · Zbl 0876.17010 · doi:10.1007/s002220050065 |
[12] | DOI: 10.1016/0021-8693(69)90007-6 · Zbl 0216.07001 · doi:10.1016/0021-8693(69)90007-6 |
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