All Questions
Tagged with applications abstract-algebra
36
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A first course in abstract algebra Fraleigh 8th ed Section 5 Exercise 65
Cracker Barrel Restaurants place a puzzle called “Jump All But One Game” at each table. The puzzle starts with golf tees arranged in a triangle as in Figure 5.29a where the presence of a tee is noted ...
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About vector spaces over finite fields [closed]
I've been dabbling with matrix computations in finite fields, and I've stumbled upon a pattern that I can't understand. Perhaps someone here could shed some light on it?
So, here's what's happening: ...
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Applications of group theory/abstract algebra [duplicate]
Before voting down, I would this text to be read.
This is not exactly a question regarding a hint to solve an exercise of a list or an exam, but a question involving the possible utility of which is ...
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Help in understanding this exercise (Linear Algebra)
I need some help in understanding the precise request of this exercise.
Let the vectors of the plane be identified with oriented segments exiting from a fixed point, and let's identify $\mathcal{V}^2$...
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How do elements in the algebraic closure of $\mathbb{Q}$ look like?
If one asks give examples of polynomial with coefficients in $\mathbb{Q}$ who don't have zeros in $Q$, simple examples given are: $x^2-3,x^3-3$. All of these have roots of form $(n)^{\frac{1}{m} }$. ...
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Prove the application $\Phi$ is bijective.
I am working on a problem set and I need some assistance with an exercise.
The exercise goes as follows:
Let $A$ be a ring and $I \unlhd A$ an ideal. Given the natural projection $\pi : A \rightarrow ...
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What is the real life application of group theory other than coding and cryptography [duplicate]
What is the real life application of group theory other than coding and cryptography if any and how can one apply group theory to them.
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What are the applications of nilpotent elements/nilpotent ideals?
As I am doing exercises related to group and ring theory I constantly see questions regarding nilpotent elements/ideals/groups. However, I have yet to see any practical use of them in theory, but I ...
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What is the applications of Lie derivations?
Let $K$ be a commutative ring with unity. Let $A$ be a unital algebra over $K$. We write $[x,y]= xy-yx$ for every $x,y \in A$ and we call it Lie product (or Lie bracket). A linear map $L: A \to A$ is ...
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Application of hyperspheres [closed]
Recently I've been studying the the volume of an n-ball. Do hyperspheres (or their volume/surface formulas) have any real-world applications?
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Real-world applications of fields, rings and groups in linear algebra.
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
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Applications of valuation rings
Some background:
I am in the process of writing a research paper for an undergraduate abstract algebra course. I've chosen to write my paper on valuation rings and discrete valuation rings. The goal ...
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what are the different applications of group theory in CS? [closed]
What are some applications of abstract algebra in computer science an undergraduate could begin exploring after a first course?
Gallian's text goes into Hamming distance, coding theory, etc., I ...
user237975
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Concrete Applications of Lattices to Algebra
The importance of lattices to algebra (or any field of mathematics really) should be fairly obvious. Specifically, we always have a complete lattice of subobjects (and a lattice of strong subobjects ...
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Application of Jordan–Hölder theorem
Jordan–Hölder theorem can be used to prove the fundamental theorem of arithmetic. But I can only prove the uniqueness part of the theorem with Jordan–Hölder theorem. That every composite number is ...
