五变量多项式代数在某些通用度类型中的可容许单项式基数

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-04-10 DOI:10.1016/j.topol.2024.108909

Nguyễn Sum

引用次数: 0

摘要

设 Pk 是二元素域 F2 上的分级多项式代数 F2[x1,x2,...,xk]，每个 xi 的度数为 1。我们研究了弗兰克-彼得森（Frank Peterson）提出的一个命题，即寻找 Pk 作为模-2 斯泰恩罗德代数 A 上模块的最小生成器集。在本文中，我们明确确定了在所有 d⩾6 的通项度数 n=2d+1-1 和 n=2d+1-2 的情况下 P5 的最小 A 生成器集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees

Let $P_{k}$ be the graded polynomial algebra $F_{2} [x_{1}, x_{2}, \dots, x_{k}]$ over the prime field of two elements, $F_{2}$ , with the degree of each $x_{i}$ being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for $P_{k}$ as a module over the mod-2 Steenrod algebra, $A$ . In this paper, we explicitly determine a minimal set of $A$ -generators for $P_{5}$ in the case of the generic degrees $n = 2^{d + 1} - 1$ and $n = 2^{d + 1} - 2$ for all $d ⩾ 6$ .

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.