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Are there any answer key of Dummit & Foote [on hold]

2

1

$begingroup$

I am trying to solve Abstract Algebra of David S. Dummit & Richard M. Foote. Almost most of the problems are statement proving type. But now I have found some counting, precisely speaking numerical answer type questions such as find out the number of prime ideals of the given ring etc. There are millions of problems of this book which are still unsolved by me. So I need a answer key to verify my work ,specialy numerical answer type questions. I have searched in Google but what I get is very naive and solved very few problems. Please provide me any accessible link of answer key , Now I am doing exercise 9.2 , so for now it's enough to get 9.2 answer key only if the whole answer key is currently unavailable.

Thanks for reading!

abstract-algebra reference-request

share|cite|improve this question

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

$endgroup$

put on hold as off-topic by rschwieb, David Hill, Martin Argerami, blub, Javi Apr 9 at 10:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – rschwieb, Martin Argerami, Javi

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $begingroup$
  There are millions of problems of this book which are still unsolved. I think this is somewhat of an exaggeration...
  $endgroup$
  – YiFan
  Mar 25 at 7:42
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  For what it's worth, I think this is an important question. Dummit & Foote is one of the better (best?) introductory algebra texts out there, so it's good if we can find an answer key for it (and a pity if we can't).
  $endgroup$
  – YiFan
  Mar 25 at 7:52
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Could you please state the problem here?
  $endgroup$
  – Wuestenfux
  Mar 25 at 8:20
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I'm voting to close this question as off-topic because it is either too broad, or asking for access to possibly copyrighted material. I can't decide which???
  $endgroup$
  – Jyrki Lahtonen
  Mar 25 at 10:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Nope, $x^3+1=(x+1)(x^2-x+1)$, but $x^2-x+1=(x-2)^2$.
  $endgroup$
  – Wuestenfux
  Mar 25 at 10:29
  

  
  
  
  

 | 
show 5 more comments

2

1

$begingroup$

I am trying to solve Abstract Algebra of David S. Dummit & Richard M. Foote. Almost most of the problems are statement proving type. But now I have found some counting, precisely speaking numerical answer type questions such as find out the number of prime ideals of the given ring etc. There are millions of problems of this book which are still unsolved by me. So I need a answer key to verify my work ,specialy numerical answer type questions. I have searched in Google but what I get is very naive and solved very few problems. Please provide me any accessible link of answer key , Now I am doing exercise 9.2 , so for now it's enough to get 9.2 answer key only if the whole answer key is currently unavailable.

Thanks for reading!

abstract-algebra reference-request

share|cite|improve this question

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

$endgroup$

put on hold as off-topic by rschwieb, David Hill, Martin Argerami, blub, Javi Apr 9 at 10:28

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – rschwieb, Martin Argerami, Javi

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  6
  

  
  
  
  
  
  

  
  $begingroup$
  There are millions of problems of this book which are still unsolved. I think this is somewhat of an exaggeration...
  $endgroup$
  – YiFan
  Mar 25 at 7:42
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  For what it's worth, I think this is an important question. Dummit & Foote is one of the better (best?) introductory algebra texts out there, so it's good if we can find an answer key for it (and a pity if we can't).
  $endgroup$
  – YiFan
  Mar 25 at 7:52
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Could you please state the problem here?
  $endgroup$
  – Wuestenfux
  Mar 25 at 8:20
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  I'm voting to close this question as off-topic because it is either too broad, or asking for access to possibly copyrighted material. I can't decide which???
  $endgroup$
  – Jyrki Lahtonen
  Mar 25 at 10:07
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Nope, $x^3+1=(x+1)(x^2-x+1)$, but $x^2-x+1=(x-2)^2$.
  $endgroup$
  – Wuestenfux
  Mar 25 at 10:29
  

  
  
  
  

 | 
show 5 more comments

$begingroup$

I am trying to solve Abstract Algebra of David S. Dummit & Richard M. Foote. Almost most of the problems are statement proving type. But now I have found some counting, precisely speaking numerical answer type questions such as find out the number of prime ideals of the given ring etc. There are millions of problems of this book which are still unsolved by me. So I need a answer key to verify my work ,specialy numerical answer type questions. I have searched in Google but what I get is very naive and solved very few problems. Please provide me any accessible link of answer key , Now I am doing exercise 9.2 , so for now it's enough to get 9.2 answer key only if the whole answer key is currently unavailable.

Thanks for reading!

abstract-algebra reference-request

share|cite|improve this question

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

$endgroup$

share|cite|improve this question

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

share|cite|improve this question

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

edited Mar 25 at 11:32

Javi

3,15321032

edited Mar 25 at 11:32

Javi

3,15321032

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

asked Mar 25 at 7:37

Subhajit SahaSubhajit Saha

284114

1 Answer
1

active

oldest

votes

1

$begingroup$

1) Looks like $Bbb Z_2[x,y]/langle x^2,y^2rangle$ with generating set $1,x,y,xy$.

2) Hint: The ideals of $Bbb Z_2[x]/langle x^3+1rangle$ are in one-to-one correspondence with the ideals of $Bbb Z_2[x]$ containing $langle x^3+1rangle$ (by one of the isomorphism theorems for rings).

share|cite|improve this answer

edited Mar 25 at 9:59

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I guess my 2nd answer is correct. Isn't it?
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  for the 1st problem $I/<x^2,y^2>$ are the ideals of the given ring .where $I = <x>, <y>, <x,y>, <x^2,y>, <x,y^2>,Z_2 (x,y), <x^2,y^2> $
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:32
  
  

  
  
  
  

add a comment | 

1

$begingroup$

1) Looks like $Bbb Z_2[x,y]/langle x^2,y^2rangle$ with generating set $1,x,y,xy$.

2) Hint: The ideals of $Bbb Z_2[x]/langle x^3+1rangle$ are in one-to-one correspondence with the ideals of $Bbb Z_2[x]$ containing $langle x^3+1rangle$ (by one of the isomorphism theorems for rings).

share|cite|improve this answer

edited Mar 25 at 9:59

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I guess my 2nd answer is correct. Isn't it?
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  for the 1st problem $I/<x^2,y^2>$ are the ideals of the given ring .where $I = <x>, <y>, <x,y>, <x^2,y>, <x,y^2>,Z_2 (x,y), <x^2,y^2> $
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:32
  
  

  
  
  
  

add a comment | 

1

$begingroup$

1) Looks like $Bbb Z_2[x,y]/langle x^2,y^2rangle$ with generating set $1,x,y,xy$.

2) Hint: The ideals of $Bbb Z_2[x]/langle x^3+1rangle$ are in one-to-one correspondence with the ideals of $Bbb Z_2[x]$ containing $langle x^3+1rangle$ (by one of the isomorphism theorems for rings).

share|cite|improve this answer

edited Mar 25 at 9:59

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I guess my 2nd answer is correct. Isn't it?
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:24
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  for the 1st problem $I/<x^2,y^2>$ are the ideals of the given ring .where $I = <x>, <y>, <x,y>, <x^2,y>, <x,y^2>,Z_2 (x,y), <x^2,y^2> $
  $endgroup$
  – Subhajit Saha
  Mar 25 at 10:32
  
  

  
  
  
  

add a comment | 

$begingroup$

1) Looks like $Bbb Z_2[x,y]/langle x^2,y^2rangle$ with generating set $1,x,y,xy$.

2) Hint: The ideals of $Bbb Z_2[x]/langle x^3+1rangle$ are in one-to-one correspondence with the ideals of $Bbb Z_2[x]$ containing $langle x^3+1rangle$ (by one of the isomorphism theorems for rings).

share|cite|improve this answer

edited Mar 25 at 9:59

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

$endgroup$

share|cite|improve this answer

edited Mar 25 at 9:59

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513

answered Mar 25 at 9:53

WuestenfuxWuestenfux

5,5131513