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Hoshino, Mitsuo; Kameyama, Noritsugu; Koga, Hirotaka

Clifford extensions. (English) Zbl 1344.16010

Commun. Algebra 44, No. 4, 1695-1703 (2016).
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

Keywords:

Auslander-Gorenstein rings; Clifford algebras; Clifford extensions; Frobenius extensions
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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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