Structure theory of central simple $Bbb{Z}_d$-graded algebras

KURTULMAZ, YOSUM; KOÇ, Cemal

Structure theory of central simple $Bbb{Z}_d$-graded algebras

Cemal KOÇ, (Doğuş Üniversitesi, Matematik Bölümü, İstanbul, Türkiye)

Yosum KURTULMAZ (Bilkent Üniversitesi, Matematik Bölümü, Ankara, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2012 Cilt: 36 Sayı: 4 Sayfa Aralığı: 560 - 577 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Structure theory of central simple $Bbb{Z}_d$-graded algebras

Öz:

This paper investigates the structure theory of $Bbb{Z}$d- central simple graded algebras and gives the complete decomposition into building block algebras. The results are also applied to generalized Clifford algebras, which are motivating examples of $Bbb{Z}$d-central simple graded algebras.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Beattie, M., Caenepeel, S.: The Brauer-Long group of $Bbb{Z}/p^{t}Bbb{Z}$-dimodule algebras. Journal of Pure and Applied Algebra 60, 219–236 (1989).
[2] Beattie, M., Caenepeel, S.: A cohomological approach to the Brauer-Long group and the groups of Galois extensions and strongly graded rings. Trans. Amer. Math. Soc. 324, 747–775 (1991).
[3] Childs, L.N., Garfinkel, G., Orzech, M.: The Brauer Group of graded Azumaya algebras. Transactions of the American Mathematical Society 175, 299–326 (1973).
[4] Van Oystaeyen, F., Zhang, Y.: Brauer groups of actions. In: Rings, Hopf Algebras, and Brauer Groups, (Eds.: S. Caenepeel and A. Verschoren) 299–326, Marcel Dekker (1998).
[5] Jacobson, N.: Lectures in Abstract Algebra, Volume II., D. Van Nostrand Company, Inc. (1953).
[6] Ko¸c, C.: Clifford algebras of d-Forms, Turkish Journal of Math., 19, 301–311 (1995).
[7] Knus, M.A.: Algebras graded by a group. Lecture Notes in Math. 92, Springer Verlag, Berlin, 117–133 (1969).
[8] Lam, T.Y.: The algebraic kheory of Quadratic Forms. W.A. Benjamin, Inc., (1973).
[9] Vela, M.: Central simple $Bbb{Z}/nBbb{Z}$-graded algebras. Communications in Algebra 30, 1995–2021 (2002).
[10] Wall, C.T.: Graded Brauer groups J. Reine Angew. Maths. 213, 187-199 (1964).
[11] Warden, V. der: Modern Algebra. Ungar (1966).

APA	KOÇ C, KURTULMAZ Y (2012). Structure theory of central simple $Bbb{Z}_d$-graded algebras. , 560 - 577.
Chicago	KOÇ Cemal,KURTULMAZ YOSUM Structure theory of central simple $Bbb{Z}_d$-graded algebras. (2012): 560 - 577.
MLA	KOÇ Cemal,KURTULMAZ YOSUM Structure theory of central simple $Bbb{Z}_d$-graded algebras. , 2012, ss.560 - 577.
AMA	KOÇ C,KURTULMAZ Y Structure theory of central simple $Bbb{Z}_d$-graded algebras. . 2012; 560 - 577.
Vancouver	KOÇ C,KURTULMAZ Y Structure theory of central simple $Bbb{Z}_d$-graded algebras. . 2012; 560 - 577.
IEEE	KOÇ C,KURTULMAZ Y "Structure theory of central simple $Bbb{Z}_d$-graded algebras." , ss.560 - 577, 2012.
ISNAD	KOÇ, Cemal - KURTULMAZ, YOSUM. "Structure theory of central simple $Bbb{Z}_d$-graded algebras". (2012), 560-577.

APA	KOÇ C, KURTULMAZ Y (2012). Structure theory of central simple $Bbb{Z}_d$-graded algebras. Turkish Journal of Mathematics, 36(4), 560 - 577.
Chicago	KOÇ Cemal,KURTULMAZ YOSUM Structure theory of central simple $Bbb{Z}_d$-graded algebras. Turkish Journal of Mathematics 36, no.4 (2012): 560 - 577.
MLA	KOÇ Cemal,KURTULMAZ YOSUM Structure theory of central simple $Bbb{Z}_d$-graded algebras. Turkish Journal of Mathematics, vol.36, no.4, 2012, ss.560 - 577.
AMA	KOÇ C,KURTULMAZ Y Structure theory of central simple $Bbb{Z}_d$-graded algebras. Turkish Journal of Mathematics. 2012; 36(4): 560 - 577.
Vancouver	KOÇ C,KURTULMAZ Y Structure theory of central simple $Bbb{Z}_d$-graded algebras. Turkish Journal of Mathematics. 2012; 36(4): 560 - 577.
IEEE	KOÇ C,KURTULMAZ Y "Structure theory of central simple $Bbb{Z}_d$-graded algebras." Turkish Journal of Mathematics, 36, ss.560 - 577, 2012.
ISNAD	KOÇ, Cemal - KURTULMAZ, YOSUM. "Structure theory of central simple $Bbb{Z}_d$-graded algebras". Turkish Journal of Mathematics 36/4 (2012), 560-577.