{"title":"代数H * (B E d)的最小生成集f2)及其应用","authors":"D. Phan, L. N. Hoang, T. K. Nguyen","doi":"10.22436/jmcs.030.01.08","DOIUrl":null,"url":null,"abstract":"We investigate the Peterson hit problem for the polynomial algebra P d , viewed as a graded left module over the mod-2 Steenrod algebra, A . For d > 4, this problem is still unsolved, even in the case of d = 5 with the help of computers. In this article, we study the hit problem for the case d = 6 in the generic degree 6 ( 2 r − 1 ) + 6.2 r , with r an arbitrary non-negative integer. Furthermore, the behavior of the sixth Singer algebraic transfer in degree 6 ( 2 r − 1 ) + 6.2 r is also discussed at the end of this paper.","PeriodicalId":45497,"journal":{"name":"Journal of Mathematics and Computer Science-JMCS","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a minimal set of generators for the algebra H ∗ ( B E d ; F 2 ) and its applications\",\"authors\":\"D. Phan, L. N. Hoang, T. K. Nguyen\",\"doi\":\"10.22436/jmcs.030.01.08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the Peterson hit problem for the polynomial algebra P d , viewed as a graded left module over the mod-2 Steenrod algebra, A . For d > 4, this problem is still unsolved, even in the case of d = 5 with the help of computers. In this article, we study the hit problem for the case d = 6 in the generic degree 6 ( 2 r − 1 ) + 6.2 r , with r an arbitrary non-negative integer. Furthermore, the behavior of the sixth Singer algebraic transfer in degree 6 ( 2 r − 1 ) + 6.2 r is also discussed at the end of this paper.\",\"PeriodicalId\":45497,\"journal\":{\"name\":\"Journal of Mathematics and Computer Science-JMCS\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics and Computer Science-JMCS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22436/jmcs.030.01.08\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics and Computer Science-JMCS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jmcs.030.01.08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a minimal set of generators for the algebra H ∗ ( B E d ; F 2 ) and its applications
We investigate the Peterson hit problem for the polynomial algebra P d , viewed as a graded left module over the mod-2 Steenrod algebra, A . For d > 4, this problem is still unsolved, even in the case of d = 5 with the help of computers. In this article, we study the hit problem for the case d = 6 in the generic degree 6 ( 2 r − 1 ) + 6.2 r , with r an arbitrary non-negative integer. Furthermore, the behavior of the sixth Singer algebraic transfer in degree 6 ( 2 r − 1 ) + 6.2 r is also discussed at the end of this paper.