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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, 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)
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### 14 Visitor Messages

1. Hi Bacterius, happy birthday!
2. Happy Birthday, Bacterius!! I hope you have a nice celebration with your close ones. . Thank you for being an active part of MHB!
3. Hey Bacterius, really liked the number theory challenge of yours. I wonder if that's an Olympiad problem. (PS : I have produced somewhat of a solution, but I am not sure if it's correct)
4. Hey, Happy Birthday! Here in the U.S., the 21st birthday in really the last milestone of youth, because that's the legal drinking age.
5. I hope that today is the beginning of a great year for you...Happy Birthday!
6. For what it's worth, you come across on the forums as someone with wisdom and maturity far beyond your years.
7. Happy Birthday!

You are no longer a teenager...it's all downhill from here.
8. Happy Birthday, mate!!
9. Happy birthday!
10. Hey Bacterius!

I thought your post in the sequence challenge was very enlightening and well-written! Excellent job!
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