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Dimension Result for the Polynomial Algebra as a Module over the Steenrod Algebra

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  • Mbakiso Fix Mothebe

Abstract

For let be the polynomial algebra in variables of degree one, over the field of two elements. The mod-2 Steenrod algebra acts on according to well-known rules. Let denote the image of the action of the positively graded part of A major problem is that of determining a basis for the quotient vector space Both and are graded where denotes the set of homogeneous polynomials of degree A spike of degree is a monomial of the form where for each In this paper we show that if and can be expressed in the form with then where is the number of spikes of degree

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  • Mbakiso Fix Mothebe, 2013. "Dimension Result for the Polynomial Algebra as a Module over the Steenrod Algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-6, December.
    • Handle: RePEc:hin:jijmms:150704
    DOI: 10.1155/2013/150704
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