Ask for example: A simple ring with zero divisors
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We know that a simple ring has characteristic either $ 0 $ or a prime $ p $. I am thinking about giving a concrete example of a simple ring WITH zero divisors.
I have found a reference talking about simple rings without zero-divisors:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/438A61A4C89B22ADF1E46E759C3A7E3D/S002557930000187Xa.pdf/div-class-title-simple-rings-without-zero-divisors-and-lie-division-rings-div.pdf
abstract-algebra ring-theory examples-counterexamples
asked Jan 10 at 5:20
user549397user549397
1,1981315
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add a comment |
$begingroup$
We know that a simple ring has characteristic either $ 0 $ or a prime $ p $. I am thinking about giving a concrete example of a simple ring WITH zero divisors.
I have found a reference talking about simple rings without zero-divisors:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/438A61A4C89B22ADF1E46E759C3A7E3D/S002557930000187Xa.pdf/div-class-title-simple-rings-without-zero-divisors-and-lie-division-rings-div.pdf
abstract-algebra ring-theory examples-counterexamples
asked Jan 10 at 5:20
user549397user549397
1,1981315
$endgroup$
$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17
add a comment |
$begingroup$
We know that a simple ring has characteristic either $ 0 $ or a prime $ p $. I am thinking about giving a concrete example of a simple ring WITH zero divisors.
I have found a reference talking about simple rings without zero-divisors:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/438A61A4C89B22ADF1E46E759C3A7E3D/S002557930000187Xa.pdf/div-class-title-simple-rings-without-zero-divisors-and-lie-division-rings-div.pdf
abstract-algebra ring-theory examples-counterexamples
asked Jan 10 at 5:20
user549397user549397
1,1981315
$endgroup$
We know that a simple ring has characteristic either $ 0 $ or a prime $ p $. I am thinking about giving a concrete example of a simple ring WITH zero divisors.
I have found a reference talking about simple rings without zero-divisors:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/438A61A4C89B22ADF1E46E759C3A7E3D/S002557930000187Xa.pdf/div-class-title-simple-rings-without-zero-divisors-and-lie-division-rings-div.pdf
abstract-algebra ring-theory examples-counterexamples
abstract-algebra ring-theory examples-counterexamples
asked Jan 10 at 5:20
user549397user549397
1,1981315
asked Jan 10 at 5:20
user549397user549397
1,1981315
asked Jan 10 at 5:20
user549397user549397
1,1981315
asked Jan 10 at 5:20
user549397user549397
1,1981315
asked Jan 10 at 5:20
user549397user549397
1,1981315
1,1981315
$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17
add a comment |
$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17
$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17
$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17
add a comment |
1 Answer
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A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple.
For instance one can take $R$ to be one's favourite field. Matrix rings
generally have zero divisors.
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple.
For instance one can take $R$ to be one's favourite field. Matrix rings
generally have zero divisors.
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
$endgroup$
add a comment |
$begingroup$
A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple.
For instance one can take $R$ to be one's favourite field. Matrix rings
generally have zero divisors.
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
$endgroup$
add a comment |
$begingroup$
A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple.
For instance one can take $R$ to be one's favourite field. Matrix rings
generally have zero divisors.
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
$endgroup$
A matrix ring $M_n(R)$ when $R$ is a simple ring, is also simple.
For instance one can take $R$ to be one's favourite field. Matrix rings
generally have zero divisors.
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
answered Jan 10 at 5:24
Lord Shark the UnknownLord Shark the Unknown
102k1159132
102k1159132
add a comment |
add a comment |
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$begingroup$
DaRT search for simple rings having zero divisors. DaRT search for simple rings with no zero divisors, other than division rings (just for kicks.)
$endgroup$
– rschwieb
Jan 10 at 14:17