On the Action of Steenrod Operations on Polynomial Algebras

İsmet KARACA

Article Details

On the Action of Steenrod Operations on Polynomial Algebras

Authors:

İsmet KARACA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 1998 Vol.22 Issue 2, pp.163-170

Document Type:

Article

Publication Date:

1/1998

Document Language:

Turkish

Document ID (Org No.):

2000749377

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

Abstract:

 

Let \bba\bba \bba  be the mod-pp p  Steenrod Algebra. Let pp p  be an odd prime number and Zp=Z/pZZp=Z/pZ Zp = Z/pZ . Let Ps=Zp[x1,x2,…,xs].Ps=Zp[x1,x2,…,xs]. Ps = Zp [x1,x2,\ldots,xs].  A polynomial N∈PsN∈Ps N \in Ps  is said to be hit if it is in the image of the action A⊗Ps\raPs.A⊗Ps\raPs. A \otimes Ps \ra Ps.  In [10] for p=2,p=2, p=2,  Wood showed that if \a(d+s)>s\a(d+s)>s \a(d+s) > s  then every polynomial of degree dd d  in PsPs Ps  is hit where \a(d+s)\a(d+s) \a(d+s)  denotes the number of ones in the binary expansion of d+sd+s d+s . Latter in [6] Monks extended a result of Wood to determine a new family of hit polynomials in Ps.Ps. Ps.  In this paper we are interested in determining the image of the action A⊗Ps\raPsA⊗Ps\raPs A\otimes Ps \ra Ps . So our results which determine a new family of hit polynomials in PsPs Ps  for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis [2], Gallant [3] and Monks [6].

 

Let \bba\bba \bba  be the mod-pp p  Steenrod Algebra. Let pp p  be an odd prime number and Zp=Z/pZZp=Z/pZ Zp = Z/pZ . Let Ps=Zp[x1,x2,…,xs].Ps=Zp[x1,x2,…,xs]. Ps = Zp [x1,x2,\ldots,xs].  A polynomial N∈PsN∈Ps N \in Ps  is said to be hit if it is in the image of the action A⊗Ps\raPs.A⊗Ps\raPs. A \otimes Ps \ra Ps.  In [10] for p=2,p=2, p=2,  Wood showed that if \a(d+s)>s\a(d+s)>s \a(d+s) > s  then every polynomial of degree dd d  in PsPs Ps  is hit where \a(d+s)\a(d+s) \a(d+s)  denotes the number of ones in the binary expansion of d+sd+s d+s . Latter in [6] Monks extended a result of Wood to determine a new family of hit polynomials in Ps.Ps. Ps.  In this paper we are interested in determining the image of the action A⊗Ps\raPsA⊗Ps\raPs A\otimes Ps \ra Ps . So our results which determine a new family of hit polynomials in PsPs Ps  for odd prime numbers generalize cononical antiautaomorphism of formulas of Davis [2], Gallant [3] and Monks [6].

Article Details

On the Action of Steenrod Operations on Polynomial Algebras

Authors:

İsmet KARACA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 1998 Vol.22 Issue 2, pp.163-170

Document Type:

Article

Publication Date:

1/1998

Document Language:

Turkish

Document ID (Org No.):

2000749377

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

22

(1998)

163-170. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.22

iss.2.

Issues

Article Details

On the Action of Steenrod Operations on Polynomial Algebras

Authors: İsmet KARACA

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 1998 Vol.22 Issue 2, pp.163-170

Document Type: Article

Publication Date: 1/1998

Document Language: Turkish

Document ID (Org No.): 2000749377

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

22

(1998)

163-170. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.22

iss.2.

Issues

Authors:

İsmet KARACA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 1998 Vol.22 Issue 2, pp.163-170

Document Type:

Article

Publication Date:

1/1998

Document Language:

Turkish

Document ID (Org No.):

2000749377

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098