İsmet KARACA

6888

On the Action of Steenrod Operations on Polynomial Algebras

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].

Anahtar Kelimeler:

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

On the Action of Steenrod Operations on Polynomial Algebras

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].

Keywords:

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

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

Sayıdaki Diğer Makaleler

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Crossed $Bbb{N}$-cubes and n- crossed complexes of commutitive algebras

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