Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 399-406 (2002)

Matrices over Centrally $\mathbb{Z}_{2}$-graded Rings

Sudarshan Sehgal, Jeno Szigeti

Department of Mathematics, University of Alberta, Edmonton, T6G 2G1, Canada, e-mail:; Institute of Mathematics, University of Miskolc, Miskolc, Hungary 3515, e-mail:

Abstract: We introduce a new computational technique for $n\times n$ matrices, over a $\Bbb{Z}_{2}$-graded ring $R=R_{0}\oplus R_{1}$ with $R_{0}\subseteq Z(R)$, leading us to a new concept of determinant, which can be used to derive an invariant Cayley-Hamilton identity. An explicit construction of the inverse matrix $A^{-1}$ for any invertible $n\times n$ matrix $A$ over a Grassmann algebra $E$ is also obtained.

Keywords: $\Bbb{Z}_{2}$-graded ring, skew polynomial ring, determinant and adjoint

Classification (MSC2000): 16A38, 15A15; 15A33

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