Unimodular commutators

Author:
Morris Newman

Journal:
Proc. Amer. Math. Soc. **101** (1987), 605-609

MSC:
Primary 15A36; Secondary 20H05

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911017-6

MathSciNet review:
911017

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Abstract: Let be a principal ideal ring and the set of matrices over . The following statments are proved: (a) If then any primitive element of occurs as the first rows of the commutator of two elements of . (b) If every element of is the product of at most commutators, then every element of is the product of at most commutators, where , and . (c) If , then every element of is the product of at most commutators, where is given in (b) above

**[1 D]**Carter and G. Keller,*Elementary expressions for unimodular matrices*, Comm. Algebra**12**(1984), 379-389. MR**737253 (86a:11023)****[2 M]**Newman,*Matrix completion theorems*, Proc. Amer. Math. Soc.**94**(1985), 39-45. MR**781052 (86d:15009)**

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0911017-6

Article copyright:
© Copyright 1987
American Mathematical Society