{"title":"环，其上的矩阵可表示为两个潜在矩阵之和","authors":"A. Abyzov, D. Tapkin","doi":"10.26907/0021-3446-2023-12-90-94","DOIUrl":null,"url":null,"abstract":"This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"1992 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rings, matrices over which are representable as the sum of two potent matrices\",\"authors\":\"A. Abyzov, D. Tapkin\",\"doi\":\"10.26907/0021-3446-2023-12-90-94\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices.\",\"PeriodicalId\":507800,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"volume\":\"1992 8\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26907/0021-3446-2023-12-90-94\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2023-12-90-94","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了在哪些条件下，场 P 中的每个元素 a 都可以表示为和 a = f + g（f q1 = f，g q2 = g，q1、q2 为大于 1 的固定整数），这意味着场 P 上的每个平方矩阵都具有类似的可表示性。作为应用，我们描述了以 2 为单位的场和交换环，在这些场和交换环上，每个平方矩阵都是两个 4 实矩阵之和。
Rings, matrices over which are representable as the sum of two potent matrices
This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices.
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