关于读书
摘要：有科研需求时集中火力阅读相关书籍 无科研需求时每天坚持阅读一个定理
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posted @ 2021-08-20 18:38
随笔分类 - 代数学
群论三经
摘要：我将《有限群论》、《有限群的特征标理论》、《代数学引论》这三本书视为群论三经。 在阅读三经过程中难免会遇到无法理解的证明或者论述，那就尽可能去弄明白；但是如果发现还是有很多困难的话，就姑且放过吧。安心地放过不懂的知识无须纠结，理由如下： 我能读懂的还有那么多，先学习自己能读懂的内容； 这三部经是要反
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posted @ 2019-05-28 10:38
关于数学学习
摘要：即日起不再写每日定理，理由是敲代码比较麻烦。所以关于数学学习的方式改为书面记录。 同时启动《有限群论》、《有限群的特征标理论》、《代数学引论》三本书。我觉得如果能把这三本书的知识吃透，做研究就不会觉得捉襟见肘了。就我目前状况而言，读书不在于多而在于精，踏踏实实地啃一啃这三本书：理解每一个定理的证明思
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posted @ 2019-05-20 17:32
Problem(1.1)
摘要：Let $V$ be an $A$-module. Show that $V$ is completely reducible iff the intersection of all of the maximal submodules of $V$ is trivial. However, this
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posted @ 2019-05-10 13:54
每日定理17
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(2.10) If $g\in G$ and $g\neq1$, then $\rho(g)=0.$ Also $\rho(1)=|G|$. Pf: Obviously. Isaac
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posted @ 2019-05-08 16:23
每日定理16
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.9) Let $\mathfrak{X}$ and $\mathfrak{Y}$ be $\mathbb{C}$-representations of a group.
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posted @ 2019-05-07 16:46
每日定理15
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(2.8) Every class function $\varphi$ of $G$ can be uniquely expressed in the form $$\varp
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posted @ 2019-05-06 10:46
每日定理14
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.6) The group $G$ is abelian iff every irreducible character is linear. Pf: The numbe
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posted @ 2019-05-04 16:24
每日定理13
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(2.5) The number $k$ of similarity classes of irreducible representations of $G$ is equ
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posted @ 2019-05-03 09:39
每日定理12
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(2.4) Let $\mathcal{K}_1,~\mathcal{K}_2,\cdots,~\mathcal{K}_r$ be the conjugacy classes o
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posted @ 2019-05-02 21:53
每日定理11
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(2.3) Pf: $tr(P^{-1}AP)=tr(A)$ $\mathfrak{X}(h^{-1}gh)=\mathfrak{X}(h)^{-1}\mathfrak{X}(g)\
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posted @ 2019-04-29 08:34
每日定理10
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Corollary(1.17) Let $A$ be a semisimple algebra over an algebraically closed field $F$ and let $
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posted @ 2019-04-28 18:51
每日定理9
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(1.16) Let $A$ be a semisimple algebra and let $M$ be an irreducible $A$-module. Let $D=E
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posted @ 2019-04-28 10:48
每日定理8
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(1.15) Let $A$ be a semisimple algebra and let $M$ be an irreducible $A$-module. Then Pf:
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posted @ 2019-04-24 16:24
每日定理7
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(1.14) Let $A$ be an $F$-algebra. Then every irreducible $A$-module is isomorphic to a fact
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posted @ 2019-04-23 09:13
每日定理6
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Lemma(1.11) Let $V$ be an $A$-module and suppose $V=\sum V_{\alpha}$ where the $V_\alpha$ are ir
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posted @ 2019-04-22 08:08
每日定理5
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(1.10) Let $V$ be an $A$-module. Then $V$ is completely reducible iff it is a sum of irre
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posted @ 2019-04-21 08:39
每日定理4
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Problems(1.9) Let $G$ be a group and $F$ a field of characteristic $p$. Suppose $p\mid|G|$, then
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posted @ 2019-04-20 08:18
关于整环的几个注记
摘要：整环中每一个素元都是不可约元 唯一分解整环上的多项式环还是唯一分解整环 整环$D$是唯一分解整环$\Leftrightarrow$$(1)$$D$中每一个真因子链都有限$(2)$$D$中每个不可约元都是素元 主理想整环中$a$为非零非单位元素：$a$素元$\Leftrightarrow$$a$不可约
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posted @ 2019-04-19 17:04
每日定理3
摘要：Isaacs, $\textit{Character Theory of Finite Groups}$, Theorem(1.9) Let $G$ be a finite group and $F$ a field whose characteristic does not divide $|G|
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posted @ 2019-04-19 08:25
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