$1-r$ unit in ring with $r^n = 0$ [duplicate]
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Units and Nilpotents
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Let $R$ be a ring with $r in R$ and $r^n = 0$ for $n in mathbb{N}$. Show that $1-r$ is a unit in $R$.
I tried to use the geometric sum but I dont know how to proceed.
abstract-algebra ring-theory
asked Nov 19 at 15:27
Arjihad
378111
marked as duplicate by rschwieb abstract-algebra
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Nov 19 at 15:31
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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Units and Nilpotents
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Let $R$ be a ring with $r in R$ and $r^n = 0$ for $n in mathbb{N}$. Show that $1-r$ is a unit in $R$.
I tried to use the geometric sum but I dont know how to proceed.
abstract-algebra ring-theory
asked Nov 19 at 15:27
Arjihad
378111
marked as duplicate by rschwieb abstract-algebra
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Nov 19 at 15:31
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
See also here.
– Bill Dubuque
Nov 19 at 15:56
add a comment |
up vote
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up vote
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This question already has an answer here:
Units and Nilpotents
3 answers
Let $R$ be a ring with $r in R$ and $r^n = 0$ for $n in mathbb{N}$. Show that $1-r$ is a unit in $R$.
I tried to use the geometric sum but I dont know how to proceed.
abstract-algebra ring-theory
asked Nov 19 at 15:27
Arjihad
378111
This question already has an answer here:
Units and Nilpotents
3 answers
Let $R$ be a ring with $r in R$ and $r^n = 0$ for $n in mathbb{N}$. Show that $1-r$ is a unit in $R$.
I tried to use the geometric sum but I dont know how to proceed.
This question already has an answer here:
Units and Nilpotents
3 answers
abstract-algebra ring-theory
abstract-algebra ring-theory
asked Nov 19 at 15:27
Arjihad
378111
asked Nov 19 at 15:27
Arjihad
378111
asked Nov 19 at 15:27
Arjihad
378111
asked Nov 19 at 15:27
Arjihad
378111
asked Nov 19 at 15:27
Arjihad
378111
378111
marked as duplicate by rschwieb abstract-algebra
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Nov 19 at 15:31
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by rschwieb abstract-algebra
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Nov 19 at 15:31
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
See also here.
– Bill Dubuque
Nov 19 at 15:56
add a comment |
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
See also here.
– Bill Dubuque
Nov 19 at 15:56
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
See also here.
– Bill Dubuque
Nov 19 at 15:56
See also here.
– Bill Dubuque
Nov 19 at 15:56
add a comment |
1 Answer
1
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oldest
votes
up vote
3
down vote
accepted
We have $(1-r)(1+r+ldots+r^{n-1}) = 1$ if $r^n=0$.
answered Nov 19 at 15:29
Wuestenfux
2,6821410
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
We have $(1-r)(1+r+ldots+r^{n-1}) = 1$ if $r^n=0$.
answered Nov 19 at 15:29
Wuestenfux
2,6821410
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
add a comment |
up vote
3
down vote
accepted
We have $(1-r)(1+r+ldots+r^{n-1}) = 1$ if $r^n=0$.
answered Nov 19 at 15:29
Wuestenfux
2,6821410
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
We have $(1-r)(1+r+ldots+r^{n-1}) = 1$ if $r^n=0$.
answered Nov 19 at 15:29
Wuestenfux
2,6821410
We have $(1-r)(1+r+ldots+r^{n-1}) = 1$ if $r^n=0$.
answered Nov 19 at 15:29
Wuestenfux
2,6821410
answered Nov 19 at 15:29
Wuestenfux
2,6821410
answered Nov 19 at 15:29
Wuestenfux
2,6821410
answered Nov 19 at 15:29
Wuestenfux
2,6821410
2,6821410
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
add a comment |
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
1
1
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
This is one of the most duplicated questions on the site. Please next time duplicate it as such instead of answering Thanks.
– rschwieb
Nov 19 at 15:32
add a comment |
That technique works. Note that it is a finite sum by your assumption.
– Randall
Nov 19 at 15:27
I dont know how to apply this correctly to the task
– Arjihad
Nov 19 at 15:29
See also here.
– Bill Dubuque
Nov 19 at 15:56