\u8fd9\u91cc\u662f\u6211\u7684\u62bd\u8c61\u4ee3\u6570\u7b14\u8bb0\u3002\u5bf9\u6211\u672c\u4eba\u6765\u8bf4\uff0c\u4f7f\u7528\u82f1\u6587\u8bb0\u7b14\u8bb0\u662f\u4e00\u6b21\u4e0d\u5c0f\u7684\u6311\u6218\uff08\u867d\u7136\u5927\u90e8\u5206\u90fd\u662f\u6284\u4e66QAQ\uff0c\u4f46\u662f\u4e5f\u5728\u4e0d\u5c11\u5730\u65b9\u5c1d\u8bd5\u6539\u6210\u81ea\u5df1\u7684\u8bed\u8a00\uff0c\u90e8\u5206\u8bc1\u660e\u4f7f\u7528\u7684\u662f\u81ea\u5df1\u7684\u65b9\u6cd5\uff09\u3002\u8fd9\u6bb5\u8bdd\u662f\u5728\u672c\u7b14\u8bb0\u5199\u5b8c\u7b2c\u4e00\u7ae0\u4e4b\u540e\u5199\u7684\uff0c\u611f\u89c9\u4e0d\u77e5\u4e0d\u89c9\u4e4b\u95f4\u5c31\u5df2\u7ecf\u8bb0\u4e86\u4e0d\u5c11\u7b14\u8bb0\u4e86\uff0c\u5728\u8fd9\u6bb5\u65f6\u95f4\u5185\u6211\u7684\u6570\u5b66\u6c34\u5e73\u4e5f\u957f\u8fdb\u4e86\u4e0d\u5c11\uff0c\u5bf9\u6570\u5b66\u4e5f\u6709\u4e86\u5168\u65b0\u7684\u8ba4\u77e5\u3002\u603b\u4e4b\uff0c\u5e0c\u671b\u4f60\u80fd\u559c\u6b22\u6211\u7684\u7b14\u8bb0\uff08\u867d\u7136\u6ca1\u6709\u4eba\u8bfb\uff09\u3002<\/p>\n
<\/p>\n
\u4ee5\u4e0b\u662f\u539f\u6587\uff1a<\/p>\n
Here is my personal note of the book, Advanced Modern Algebra<\/em>, written by Joseph J. Rotman. It’s the second time I try to write a note concerning abstract algebra. Maybe this article contains many faults, and if you find some of them, please leave a comment to let me know. Please note that some of the math marks in this article do not use the same mark as in the book, because of the habit of mine.<\/p>\n Abstract algebra is an important part of modern mathematics. It is the study of algebra structures, such as groups, rings and fields etc. It concentrates on the common properties of algebra structures instead of certain numbers or equations. It’s the basis for learning many fields of mathematics.<\/p>\n Change log<\/strong>:<\/p>\n Contents:<\/strong><\/p>\n \u8fd9\u91cc\u662f\u6211\u7684\u62bd\u8c61\u4ee3\u6570\u7b14\u8bb0\u3002\u5bf9\u6211\u672c\u4eba\u6765\u8bf4\uff0c\u4f7f\u7528\u82f1\u6587\u8bb0\u7b14\u8bb0\u662f\u4e00\u6b21\u4e0d\u5c0f\u7684\u6311\u6218\uff08\u867d\u7136\u5927\u90e8\u5206\u90fd\u662f\u6284\u4e66QAQ\uff0c\u4f46\u662f\u4e5f\u5728\u4e0d\u5c11\u5730 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12,6],"tags":[11,8],"class_list":["post-361","post","type-post","status-publish","format-standard","hentry","category-abstract-algebra","category-6","tag-11","tag-8"],"_links":{"self":[{"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/posts\/361","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/qwq.cafe\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=361"}],"version-history":[{"count":22,"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/posts\/361\/revisions"}],"predecessor-version":[{"id":418,"href":"https:\/\/qwq.cafe\/index.php?rest_route=\/wp\/v2\/posts\/361\/revisions\/418"}],"wp:attachment":[{"href":"https:\/\/qwq.cafe\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=361"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qwq.cafe\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=361"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qwq.cafe\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=361"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n
\n1.1 Polynomials<\/a>
\n1.2 Homomorphisms<\/a>
\n1.3 Quotient Rings<\/a>
\n1.4 From Arithmetic to Polynomials<\/a>
\n1.5 Maximal Ideals and Prime Ideals<\/a>
\n1.6 Finite Fields<\/a>
\n1.7 Irreducibility<\/a>
\n1.8 Euclidean Rings and Principal Ideal Domains<\/a>
\n1.9 Unique Factorization<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"