Dimension result for the polynomial algebra of six variables as a module over steenrod algebra in some degree
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tinnk@hcmute.edu.vnTừ khóa:
Steenrod squares, polynomial algebra, hit problem, algebraic transfer, Steenrod algebraTóm tắt
Let be the graded polynomial algebra with the degree of each generator being 1, where denote the prime field of two elements. We study the hit problem set up by Frank Peterson of finding a minimal set of generators for the polynomial algebra as a module over the mod-2 Steenrod algebra, . If we consider as a trivial -module, then the hit problem is equivalent to the problem of finding a basis of -graded vector space . The problem is still open for . It is known that the hit problem is reduced to the case of the degree u of the form , where are non-negative integers such that Here, is the smallest number for which it is possible to write , where . In this paper, we study the hit problem of the degree in for any integer .
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