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Dimension Result for the Polynomial Algebra ?2[x1,…,xn] as a Module over the Steenrod Algebra
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-19
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
For n≥1, let P(n)=?2[x1,…,xn] be the polynomial algebra in n variables xi, of degree one, over the field ?2 of two elements.
The mod-2 Steenrod algebra ? acts on P(n) according to well-known rules.
Let ?+P(n) 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 Q(n)=P(n)/?+P(n).
Both P(n)=⊕d≥0Pd(n) and Q(n) are graded where Pd(n) denotes the set of homogeneous polynomials of degree d.
A spike of degree d is a monomial of the form x12λ1-1⋯xn2λn-1 where λi≥0 for each i.
In this paper we show that if n≥2 and d≥1 can be expressed in the form d=d(λ)=(n-1)(2λ-1) with λ≥2, then dim(Qd(λ)(n))≥B(n,d(λ))+{∑q=2λ(nq), if λ
American Psychological Association (APA)
Mothebe, Mbakiso Fix. 2013. Dimension Result for the Polynomial Algebra ?2[x1,…,xn] as a Module over the Steenrod Algebra. International Journal of Mathematics and Mathematical Sciences،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-449814
Modern Language Association (MLA)
Mothebe, Mbakiso Fix. Dimension Result for the Polynomial Algebra ?2[x1,…,xn] as a Module over the Steenrod Algebra. International Journal of Mathematics and Mathematical Sciences No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-449814
American Medical Association (AMA)
Mothebe, Mbakiso Fix. Dimension Result for the Polynomial Algebra ?2[x1,…,xn] as a Module over the Steenrod Algebra. International Journal of Mathematics and Mathematical Sciences. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-449814
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-449814