The unit group of algebra of circulant matrices

Document Type: Research Paper

Authors

1 Indian Institute of Technology Delhi Hauz Khas, New Delhi-110016 India

2 Indian Institute of Technology Delhi Hauz Khas, New Delhi India

Abstract

Let $Cr_{n}(F)$ denote the algebra of $n\times n$ circulant matrices over the field $F$‎. ‎In this paper‎, ‎we study the unit group of $Cr_{n}(\mathbb{F}_{p^{m}})$‎, ‎where $\mathbb{F}_{p^{m}}$ denotes the Galois field of order $p^{m},~p$ prime‎.

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V. Bovdi (2001). On symmetric units in group algebras. Comm. Algebra. 29 (12), 5411-5422
V. Bovdi (2012). Group rings in which the group of units is hyperbolic. J. Group Theory. 15 (2), 227-235
L. Creedon and J. Gildea (2011). The Structure of the Unit Group of the Group Algebra F_2^k D_8. Canad. Math. Bull.. 54 (2), 237-243
J. Gildea (2008). The special circulant matrix and units in group rings. Acta Math. Acad. Paedagog. Nyhazi.. 24 (2), 221-225
J. Gildea (2010). The structure of the unit group of the group algebra F_3^k(C_3 D_6). Comm. Algebra. 38 (9), 3311-3317
J. Gildea (2011). Units of the group algebra F_2^k(C_2 D_{8). J. Algebra Appl.. 10 (4), 643-647
T. Hurley (2006). Group rings and rings of matrices. Int. J. Pure Apl. Math.. 31 (3), 319-335
K. Kaur and M. Khan (2014). Units in F_2 D_2p. J. Algebra Appl., http://dx.doi.org/10.1142/S0219498813500904. 13 (2)
R. Lidl and H. Niederreiter (2000). Finite Fields. Cambridge University Press.
S. Perlis and G. L. Walker (1950). Abelian group algebras of finite order. Trans. Amer. Math. Soc.. 68 (3), 420-426
C. P. Milies and S. K. Sehgal (2002). An Introduction to Group Rings. Kluwer Academic Publishers.
R. K. Sharma and P. Yadav (2013). Unit group of algebra of circulant matrices. Int. J. Group Theory. 2 (4), 1-6
R. K. Sharma, P. Yadav and K. Joshi (2012). Units in Z_2 (C_2times D_{infty}). Int. J. Group Theory. 1 (4), 33-41