Unformatted text preview: (b) Show that G is isomorphic to either Z /p 2 or Z /p × Z /p . (5) Let M 2 ( R ) be the set of 2 × 2 matrices with entries in R . Then M 2 ( R ) is a ring with the usual matrix addition and matrix multiplication. (a) Show that °± a b − b a ² : a, b ∈ R ³ is a subring of M 2 ( R ). (b) Show that the center of M 2 ( R ) is Z ( M 2 ( R )) = { λI 2 : λ ∈ R } where I 2 is the 2 × 2 identity matrix. Department of Mathematics, McGill University, Montreal, QC, H3A 2K6 Canada Email address : [email protected] 1...
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 Fall '07
 Goren
 Algebra, Ring, Email address, Let M2

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