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• Yesterday, 06:39
I am reading T. S. Blyth's book: Module Theory: An Approach to Linear Algebra ... I am focused on Chapter 2: Submodules; intersections and sums...
0 replies | 32 view(s)
• Yesterday, 03:00
In Chapter 1 of his book: "Modules and Rings", John Dauns (on page 7) considers a subset T of an R-module M and defines the R-submodule generated by...
0 replies | 35 view(s)
• Yesterday, 00:27
Hi steenis ... despite your help (thank you) ... I have not been able to make much progress on the converse ... see below ... Converse: ...
14 replies | 240 view(s)
• May 24th, 2018, 16:00
MarkFL replied to a thread Word problem on vectors in Geometry
Hello, and welcome to MHB, Gummg! (Wave) I would write the plane's velocity vector as: \vec{v}=485\left\langle...
3 replies | 78 view(s)
• May 23rd, 2018, 11:43
Here is this week's POTW: ----- Prove that there are only a finite number of possibilities for the ordered triple $(a-b,\,b-c,\,c-a)$ where...
0 replies | 67 view(s)
• May 23rd, 2018, 11:40
Congratulations to the following members for their correct solution:): 1. Olinguito 2. Opalg Solution from Opalg: If...
1 replies | 104 view(s)
• May 23rd, 2018, 07:55
Now consider \phi \ : \ M^{(\Delta)} = \bigoplus_\Delta M_\alpha \to N Let ( x_\alpha ) \in \bigoplus_\Delta M_\alpha ... Then by...
14 replies | 240 view(s)
• May 23rd, 2018, 07:01
Thanks ... OK now ... Peter
14 replies | 240 view(s)
• May 23rd, 2018, 06:47
Thanks again steenis ... ... But ... just a clarification ... $f \neq 0$, so there is a $y \in N$ with $f(x) \neq 0$. ... ... " Did you...
14 replies | 240 view(s)
• May 23rd, 2018, 06:15
14 replies | 240 view(s)
• May 23rd, 2018, 01:07
Thanks for the advice ...!!! We are trying to show that M \text{ generates } N \Longrightarrow for each non-zero R-linear mapping f \ : \ N...
14 replies | 240 view(s)
• May 22nd, 2018, 14:03
Here's the image you tried to hotlilnk:
4 replies | 97 view(s)
• May 22nd, 2018, 00:46
I would take Greg's advice and write: 5\sqrt{2}\pm7=(b\sqrt{2}\pm a)^3=\pm...
5 replies | 146 view(s)
• May 22nd, 2018, 00:40
I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need...
0 replies | 53 view(s)
• May 21st, 2018, 09:57
Thanks Steenis ... Late now in southern Tasmania (edge of the world 😌 Strong winds ... 115 km per hour roaring round my old house ... ) Will...
14 replies | 240 view(s)
• May 21st, 2018, 07:00
Thanks for the correction, Steenis ... ... ... and thanks for all your help with this problem ... Peter
8 replies | 163 view(s)
• May 21st, 2018, 03:35
I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.1 Generating and Cogenerating Classes ... ......
14 replies | 240 view(s)
• May 21st, 2018, 01:32
Hi Steenis ... thanks ... Have taken note of the points you have made ... We have to show that ( \bigoplus_\Delta M_\alpha ) / (...
8 replies | 163 view(s)
• May 20th, 2018, 23:49
Where does "it" say that?
11 replies | 17728 view(s)
• May 20th, 2018, 00:53
Hi Steenis ... The obvious R-map between $M$ and $M/N$ is the canonical surjection or natural map \eta \ : \ M \rightarrow M/N ... ... defined...
8 replies | 163 view(s)
• May 19th, 2018, 00:17
Thanks for the help, Steenis ... Hmm ... but still not sure how to proceed ... Can you help a bit further ... Peter
8 replies | 163 view(s)
• May 18th, 2018, 23:41
Thanks for all the help, Steenis ... thanks to you I understand a lot more than when I started working on the problem ... Regarding the last few...
37 replies | 675 view(s)
• May 18th, 2018, 02:34
Let M and N be R-modules ... We want to show that: M generates N \Longleftrightarrow \exists a subset H \subseteq \text{ Hom }_R (M, N)...
37 replies | 675 view(s)
• May 17th, 2018, 06:06
Oh Lord ... forgot the converse ... !!! Had gone onto something else ... see new problem ... But will return to converse... Peter
37 replies | 675 view(s)
• May 17th, 2018, 06:02
I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need...
8 replies | 163 view(s)
• May 17th, 2018, 05:44
Thanks for those points of improvement ... The previously polluted notation ... :) ... was a helpful lesson for me ... Thanks for all your help...
37 replies | 675 view(s)
• May 17th, 2018, 05:19
Let M and N be R-modules ... We want to show that: M generates N \Longleftrightarrow \exists a subset H \subseteq \text{ Hom }_R (M, N) such...
37 replies | 675 view(s)
• May 16th, 2018, 20:53
MarkFL replied to a thread Jokes in Chat Room
175 replies | 24424 view(s)
• May 16th, 2018, 08:14
Getting late here in Tasmania ... Will start again on this tomorrow morning ... Thank you for all your explanations, guidance and help ... ...
37 replies | 675 view(s)
• May 16th, 2018, 08:05
f_\alpha = f \circ i_\alpha so f_\alpha \ : \ M_\alpha \rightarrow N ... so f_\alpha maps M_\alpha = M into N ... ... hence I think we can then...
37 replies | 675 view(s)
• May 16th, 2018, 07:52
Hi Steenis, Just a further clarification ... how do we know $\Sigma_H \text{ im } f \subset N$ ... indeed why/how is this true ... Hope you...
37 replies | 675 view(s)
• May 16th, 2018, 07:39
Hi Steenis ... thanks for explaining that ... so if I'm right we have an epimorphism f and a dummy variable f ... Peter
37 replies | 675 view(s)
• May 16th, 2018, 07:09
Thanks Steenis ... but just a clarification ... You write: " ... ... \Sigma_H \text{ im } f = \Sigma \{ \text{ im } f | f \in H \} ......
37 replies | 675 view(s)
• May 16th, 2018, 06:37
Hi Steenis ... Regarding the above post ... you write: " ... ... \$N = \Sigma_H \text{ im } f = \Sigma \{ \text{ im } f | f \in H \} =...
37 replies | 675 view(s)
More Activity

### 17 Visitor Messages

1. Hello and welcome back to MHB, Deveno!

We are happy to see that you have returned, and we look forward to your continued participation here!

On Behalf Of MHB's Staff,

anemone.
2. Hi Deveno ... ... Hope you return to MHBs soon ... you are sadly missed ...

Peter
3. Hi Deveno ... haven't seen you for a while ... hope all is well with you ...

Best regards,

Peter
4. Hi Deveno,

work has taken me out of the state of Tasmania and into regional Victoria ... about 150kms outside Melbourne ...

Should re-establish broadband links and get some time in a day or so ...

Thanks as always for you help ...

Peter
5. Hello and welcome back to MHB, Deveno!

We are happy to see that you have returned, and we look forward to your continued participation here!

On Behalf Of MHB's Staff,

anemone.
6. Good answers on Peter's questions, and well-given exercises too. Unfortunately though I wouldn't be able to check Peter's work on the matrix algebras. Every ring is commutative to me
7. Thanks a bunch, I'll see if I can play through your ideas.
8. Hello, David, what d'you think of the group theoretic analogy of galois theory I have posted in the abstract algebra forum? Can this thing be arrow-theoretically generalized to categories too?
9. I'm a little late but congratulations on 1k posts! Really happy to have you at MHB and here's a toast to the next 1k.
10. excellent respond to the "how do you add and subtract measurements" thread. i would not have had the energy to go through all of that step by step like that.
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