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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 6

Question

Math 6310 • Algebra Fall 1998 • Question 6

Prove Wedderburn’s theorem: if the ring \(R\) has a faithful simple module that is finite-dimensional over its commutant ring, then \(R\cong M_n(D)\) for some \(n\ge 1\), where \(D\) is a division ring.

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Prove Wedderburn's theorem: if the ring \(R\) has a faithful simple module that is
finite-dimensional over its commutant ring, then \(R\cong M_n(D)\) for some \(n\ge 1\), where \(D\) is
a division ring.

Topic Tags

Ideals and Quotient Rings Modules over PIDs