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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
micromass
1 30,530
I am trying to understand the concept of a k-algebra without much success. Can someone please give me a clear...
Feb2-13 11:36 AM
mathwonk
1 514
I am reading Dummit and Foote Chapter 7. D&F use a quadratic field as an example of a ring. I am trying to get a...
Jan21-12 03:33 AM
Math Amateur
7 1,187
I am reading James and Liebeck's book on Representations and Characters of Groups. Exercise 1 of Chapter 3 reads as...
Jan21-12 08:59 PM
Math Amateur
2 1,274
I am reading Kane - Reflection Groups and Invariant Theory and need help with two of the properties of reflections...
Mar28-12 08:19 PM
morphism
1 892
I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6...
Apr22-12 05:46 PM
Math Amateur
4 1,022
I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and...
Oct30-13 10:52 PM
Math Amateur
2 401
I was having a quick look at Isaacs : Algebra - A Graduate Course and was interested in his approach to Noetherian...
Oct31-13 01:02 AM
R136a1
3 419
I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and...
Oct30-13 11:54 PM
Math Amateur
2 400
I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a...
Nov3-13 01:28 AM
Math Amateur
2 445
I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a...
Nov2-13 09:37 AM
R136a1
1 413
I am reading Dummit and Foote: Section 15.2 Radicals and Affine Varieties. On page 678, Proposition 16 reads as...
Nov3-13 08:06 AM
R136a1
3 497
In Dummit and Foote Chapter 15, Section 15.3: Radicals and Affine Varieties on page 679 we find the following...
Nov8-13 12:53 AM
Math Amateur
2 442
In Dummit and Foote, Chapter 15, Section 15.2 Radicals and Affine Varieties, Example 2, page 681 begins as follows: ...
Nov9-13 01:39 PM
R136a1
1 487
I have a problem in understanding the proof to Dummit and Foote Section 15.2, Proposition 19 regarding primary ideals....
Nov9-13 01:36 PM
R136a1
1 503
I am studying Dummit and Foote Section 15.2. I am trying to understand the proof of Proposition 19 Part (5) on page...
Nov10-13 01:42 AM
R136a1
4 460
In Dummit and Foote on page 682 Example 1 reads as follows:...
Nov11-13 03:53 PM
Math Amateur
2 461
Example (2) on page 682 of Dummit and Foote reads as follows: ...
Nov12-13 03:34 PM
Math Amateur
2 462
Example (2) on page 682 of Dummit and Foote reads as follows: (see attached) ...
Nov13-13 02:22 PM
mathwonk
4 525
Hi, can someone please explain to me what "modding out by A" means? R is ring and A is subring of R R/A = {r+A|r in...
Nov27-05 08:40 PM
mathwonk
4 2,264
I just finished learning about Sylow theorems and I have a quick question and was wondering if someone could help me...
Mar2-06 02:30 PM
matt grime
10 2,566
Few days ago, I was thinking about why we need to define V*=Hom(V,K) for a K-vector space when the dimension of V is...
Oct24-13 07:16 PM
WWGD
2 503
I'm preparing for an upcoming exam, and as I see one of the typical questions that is frequently asked in our exams is...
Nov2-13 09:54 AM
R136a1
1 528
When explicitly given a set of polynomial equations, I am interested in describing its singular locus. I read this...
Feb18-12 01:23 AM
Norwegian
1 1,101
so factor groups/quotient groups have been tripping me up recently and if i could a definition and maybe an example...
May30-10 05:43 PM
VeeEight
1 947
hi friends can someone help me and explain for me what is the difference between a standard and metric?
Nov11-10 08:21 AM
HallsofIvy
5 853
Hello friends, I am looking for an idea to my exercise! let's E be a vector space, e_ {i} be a basis of E, b_ {a}...
Feb4-13 08:02 AM
HallsofIvy
2 635
If F is a field, how do we prove that a non-zero polynomial with coefficients in F and of degree n has at most n...
May18-08 06:19 PM
mathwonk
2 2,949
If A and B are subgroups of G and AB=G does it follow that AB=BA? If yes, why?
Oct1-08 04:13 PM
sutupidmath
8 981
I'd like to show that is sequentially compact. So I pick a sequence in , say (xn). case 1:range(xn) is finite...
Oct21-08 04:01 PM
morphism
1 1,917
Any pointers and/or help with proving the following would be appreciated For every prime number n, there exist...
Jan1-10 10:04 PM
ramsey2879
2 1,739
Problem: Prove that every vector space V has maximal subspace, i.e. a proper subspace that is not properly contained...
Dec5-07 06:17 PM
mathboy
10 2,847
Hi everyone. I am not sure if this problem belongs under the "Linear & Abstract algebra" section but it seemed like it...
Feb17-09 02:19 PM
mathclass
4 4,626
Help needed to eventually understand Quotient spaces.
Feb12-08 04:23 PM
mrandersdk
8 2,411
Hello all. I wasd beginning to feel at home with vectors and covectors but while trying to fully understand the...
Jun20-07 06:54 AM
matt grime
25 4,578
Hello all. I am in need of a quick clarification. A text I am reading describes an ideal in a ring as 'analogous'...
Aug1-07 07:57 PM
matheinste
7 2,097
Hello all. I reluctantly ask this question because it is probably,as the text states easy, but my desire to clear...
Aug3-07 01:24 PM
matheinste
6 1,576
Hello everyone. I came across the term free vector space in a book on mathematical physics by Geroch but cannot...
Dec30-07 12:08 PM
mathwonk
11 9,682
Hello all. Back to basics again. When defining a set of geometric vectors for a vector space of n dimensions how...
Dec11-07 05:39 PM
matheinste
9 1,566
Hello all. I am reading again about free vector spaces over a set. In the Theory of Groups by Kurosh part of the...
Dec24-07 10:50 AM
mathwonk
6 1,973
Hello all. Most modern treatments of the tensor product use equivalence classes to define a quotient space in order...
Feb25-09 11:52 AM
fisicoloko
11 3,422

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