Turkish Journal

of

Mathematics

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# Turkish Journal of Mathematics

On the Action of Steenrod Operations on Polynomial Algebras

Ýsmet KARACA
Lehigh University,
Bethlehem, PA 18015-USA

Abstract: Let $$\bba$$ be the mod-$$p$$ Steenrod Algebra. Let $$p$$ be an odd prime number and $$Zp = Z/pZ$$. Let $$Ps = Zp [x1,x2,\ldots,xs].$$ A polynomial $$N \in Ps$$ is said to be hit if it is in the image of the action $$A \otimes Ps \ra Ps.$$ In [10] for $$p=2,$$ Wood showed that if $$\a(d+s) > s$$ then every polynomial of degree $$d$$ in $$Ps$$ 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 $$Ps.$$ In this paper we are interested in determining the image of the action $$A\otimes Ps \ra Ps$$. So our results which determine a new family of hit polynomials in $$Ps$$ for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis [2], Gallant [3] and Monks [6].

Turk. J. Math., 22, (1998), 163-170.
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Other articles published in the same issue: Turk. J. Math.,vol.22,iss.2.