{"title":"梅森-斯托瑟斯定理","authors":"Manuel Eberl","doi":"10.1090/mbk/121/69","DOIUrl":null,"url":null,"abstract":"A child learns of the nonnegative numbers at an early age. Polynomials, on the other hand, demand a little more sophistication and are reserved in a U.S. child’s education for middle school. Those fortunate enough to take an undergraduate abstract algebra class realize that the chasm between the integers and polynomials is not so vast. One learns there are similarities: both integers and polynomials form rings; and that there are analogies: the integers have prime factors as their basic building blocks, whereas polynomials (over C) have linear factors. Given this, it is not that surprising that we have the following definitions:","PeriodicalId":423691,"journal":{"name":"100 Years of Math Milestones","volume":"30 4","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Mason–Stothers theorem\",\"authors\":\"Manuel Eberl\",\"doi\":\"10.1090/mbk/121/69\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A child learns of the nonnegative numbers at an early age. Polynomials, on the other hand, demand a little more sophistication and are reserved in a U.S. child’s education for middle school. Those fortunate enough to take an undergraduate abstract algebra class realize that the chasm between the integers and polynomials is not so vast. One learns there are similarities: both integers and polynomials form rings; and that there are analogies: the integers have prime factors as their basic building blocks, whereas polynomials (over C) have linear factors. Given this, it is not that surprising that we have the following definitions:\",\"PeriodicalId\":423691,\"journal\":{\"name\":\"100 Years of Math Milestones\",\"volume\":\"30 4\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"100 Years of Math Milestones\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mbk/121/69\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"100 Years of Math Milestones","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mbk/121/69","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A child learns of the nonnegative numbers at an early age. Polynomials, on the other hand, demand a little more sophistication and are reserved in a U.S. child’s education for middle school. Those fortunate enough to take an undergraduate abstract algebra class realize that the chasm between the integers and polynomials is not so vast. One learns there are similarities: both integers and polynomials form rings; and that there are analogies: the integers have prime factors as their basic building blocks, whereas polynomials (over C) have linear factors. Given this, it is not that surprising that we have the following definitions:
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