All Questions
Tagged with abstract-algebra applications
36
questions
2
votes
0
answers
66
views
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 ...
-1
votes
1
answer
63
views
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: ...
2
votes
0
answers
76
views
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 ...
1
vote
1
answer
57
views
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 $\mathcal{V}^2$...
1
vote
1
answer
49
views
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 $(n)^{\frac{1}{m} }$. ...
1
vote
0
answers
72
views
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 ...
-1
votes
1
answer
272
views
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.
1
vote
1
answer
551
views
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 ...
0
votes
1
answer
57
views
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 ...
-2
votes
1
answer
65
views
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?
5
votes
3
answers
2k
views
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 ...
8
votes
2
answers
987
views
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 ...
42
votes
11
answers
24k
views
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 ...
6
votes
1
answer
184
views
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 ...
1
vote
0
answers
378
views
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 ...