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J. Aust. Math. Soc.
76 (2004), 317-328 | ||||||||
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On decomposition of sub-linearised polynomials
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| Abstract | ||||||||
| We give a detailed exposition of the theory of
decompositions of linearised polynomials, using a
well-known connection with skew-polynomial rings
with zero derivative. It is known that there is a
one-to-one correspondence between decompositions
of linearised polynomials and sub-linearised
polynomials. This correspondence leads to a
formula for the number of indecomposable
sub-linearised polynomials of given degree over a
finite field. We also show how to extend existing
factorisation algorithms over skew-polynomial
rings to decompose sub-linearised polynomials
without asymptotic cost.
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