Turkish Journal of Mathematics
DOI
-
Abstract
Let \( \bba \) be the mod-\( p \) Steenrod Algebra. Let \( p \) be an odd prime number and \( Z_{p} = Z/pZ \). Let \( P_{s} = Z_{p} [x_{1},x_{2},\ldots,x_{s}]. \) A polynomial \( N \in P_{s} \) is said to be hit if it is in the image of the action \( A \otimes P_{s} \ra P_{s}. \) In [10] for \( p=2, \) Wood showed that if \( \a(d+s) > s \) then every polynomial of degree \( d \) in \( P_{s} \) is hit where \( \a(d+s) \) denotes the number of ones in the binary expansion of \( d+s \). Latter in [6] Monks extended a result of Wood to determine a new family of hit polynomials in \( P_{s}. \) In this paper we are interested in determining the image of the action \( A\otimes P_{s} \ra P_{s} \). So our results which determine a new family of hit polynomials in \( P_{s} \) for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis [2], Gallant [3] and Monks [6].
First Page
163
Last Page
170
Recommended Citation
KARACA, İ. (1998) "On the Action of Steenrod Operations on Polynomial Algebras," Turkish Journal of Mathematics: Vol. 22: No. 2, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol22/iss2/4
