# Tagged Questions

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### Suggestions for choice of abstract algebra project [closed]

I want to know which of these topics have more materials and is interesting to write my project on... Group action as an extension of group multiplication or Wreath products of cyclic groups
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### What is subtraction?

Let $a, b \in \mathbf{R}$. It is an elementary fact that addition is a commutative binary operation on the reals, that is, $a + b \in \mathbf{R}$ and $a + b = b + a$. With the exception of ...
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### A city wants to encourage downtown

could you please help me with this ( part d ) A city wants to encourage downtown employees to use public transportation. Below is the time in minutes to get to work on one morning according to ...
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### Text on Witt vectors that are accessible to undergraduate students

I am looking for a thorough text on Witt vectors that is accessible to an undergraduate student that have completed the following courses: Calc 1, 2, Linear Algebra and Abstract Algebra. (In Norway, ...
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### a second course in abstract algebra

I recently read an abstract algebra textbook, "A first course in abstract algebra" by John Fraleigh. I am interested in continuing to do some more self studying. What is a good book for a second ...
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### Soft question (Etymology - Flatness)

Why where flat modules named "flat"? Is it because they are necessarily torsion free so in a "not convoluted" or circular like $\mathbb{Z}/n\mathbb{Z}$ is as a $\mathbb{Z}$-module?
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### How is addition different than multiplication?

Is there a fundamental difference in the things we call multiplication and those we call addition? In a field, both binary operations obey exactly the same rules (commutativity, associativity, ...
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### Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
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### Is it bad to keep aside Lang's Algebra in graduate school?

Question is as it is stated in title. I will be joining for PhD program in this July 2014. I am interested in working in Algebra/Algebraic Geometry/Algebraic Number Theory. I tried to learn algebra ...
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### Applications of groups, rings and modules in life [closed]

I have read calculus. Now I'm reading algebra. What is the application of groups, rings and modules in life? When we study derivations we know several applications. What about groups, rings and ...
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### Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
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### Why are groups “abelian” but rings “commutative”?

I have never seen, in any text, a ring whose multiplication is commutative being called an "abelian ring", even though this would make perfect sense, because this term would necessarily refer to ...
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### Subgroup Lattices and Dimension

I apologize in advance in the case that this question is nonsensical. If the idea isn't clear, I can perhaps explain more below. In the fall I am taking an undergraduate abstract algebra course, and ...
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### Why is abstract algebra so important?

In my studies of physics and mathematics, I have encountered a fair bit of geometry, Lie group and representation theory, and real and complex analysis and I understand why these branches of ...
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### definitions in algebra

I am interested in algebra and I want to read some good books about it. I have a problem with some definitions like free group or algebra. In some books there are different definitions of them and I'm ...
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### Commutative/noncommutative algebra?

I know basic knowledge of undergraduate algebra till galois theory of finite extensions. I want to learn number theory, but also like algebra. This semester I have to choose to read either commutative ...
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### What's the exact meaning of this sentence from George Peacock?

I am reading the book "A history of abstract algebra" by Israel Kleiner. The following sentence is said by George Peacock. I am not a native English speaker. So could someone translate it into plain ...
I know that : if two subgroups of $G$ are conjugate then they are isomorphic. Howerver , I also know that the converse is not always true. I often understand a mathematical structure only trough ...
Show that the set of all real numbers of the form $a_0 + a_1\pi + a_2\pi^2 +\cdots+ a_n\pi^n$ with $n≥0$ and $a_i ∈ \mathbb{Z}$ is a subring of $R$ that contains $\mathbb{Z}$ and $\pi$. ...