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| Paper IPM / M / 18016 |
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| Abstract: | |
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Let F be a field, p(x) be a quadratic polynomial in F[x]
with a non-zero constant term, and nâ¥2 be a positive integer. We say that TâMn(F) is p(x)-quadratic if p(T)=0. In this paper, given AâSLn(F), we show that A can be decomposed into a product of at most two commutators of p(x)-quadratic matrices if either p(x) has two distinct roots in F and A is non-scalar, or if F is algebraically closed and has characteristic different from 2. A similar result for matrices over real quaternion division rings is also provided.
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