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Some Relations between Admissible Monomials for the Polynomial Algebra

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  • Mbakiso Fix Mothebe
  • Lafras Uys

Abstract

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. A major problem in algebraic topology is of determining , the image of the action of the positively graded part of . We are interested in the related problem of determining a basis for the quotient vector space . has been explicitly calculated for but problems remain for . Both and are graded, where denotes the set of homogeneous polynomials of degree . In this paper, we show that if is an admissible monomial (i.e., meets a criterion to be in a certain basis for ), then, for any pair of integers ( ), , and , the monomial is admissible. As an application we consider a few cases when .

Suggested Citation

  • Mbakiso Fix Mothebe & Lafras Uys, 2015. "Some Relations between Admissible Monomials for the Polynomial Algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-7, August.
    • Handle: RePEc:hin:jijmms:235806
    DOI: 10.1155/2015/235806
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