Identity element in non-associative ring
$begingroup$
It is said, that if both a left identity and a right identity in associative ring exists, then it is a two-sided identity as $$e_1=e_1*e_2=e_2$$
Why is associativity required for this property?
abstract-algebra associativity
asked Dec 5 '18 at 14:52
ACartashACartash
132
$endgroup$
add a comment |
$begingroup$
It is said, that if both a left identity and a right identity in associative ring exists, then it is a two-sided identity as $$e_1=e_1*e_2=e_2$$
Why is associativity required for this property?
abstract-algebra associativity
asked Dec 5 '18 at 14:52
ACartashACartash
132
$endgroup$
add a comment |
$begingroup$
It is said, that if both a left identity and a right identity in associative ring exists, then it is a two-sided identity as $$e_1=e_1*e_2=e_2$$
Why is associativity required for this property?
abstract-algebra associativity
asked Dec 5 '18 at 14:52
ACartashACartash
132
$endgroup$
It is said, that if both a left identity and a right identity in associative ring exists, then it is a two-sided identity as $$e_1=e_1*e_2=e_2$$
Why is associativity required for this property?
abstract-algebra associativity
abstract-algebra associativity
asked Dec 5 '18 at 14:52
ACartashACartash
132
asked Dec 5 '18 at 14:52
ACartashACartash
132
asked Dec 5 '18 at 14:52
ACartashACartash
132
asked Dec 5 '18 at 14:52
ACartashACartash
132
asked Dec 5 '18 at 14:52
ACartashACartash
132
132
add a comment |
add a comment |
1 Answer
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$begingroup$
Nobody said associativity was required.
You can search the web and find the phrase "nonassociative ring with unity" used, and see their examples.
In fact, I think you can just take any nonassociative ring $R$ and perform the standard Dorroh construction on $mathbb Ztimes R$ to get a nonassociative ring with identity.
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
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1 Answer
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1 Answer
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active
oldest
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active
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active
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votes
$begingroup$
Nobody said associativity was required.
You can search the web and find the phrase "nonassociative ring with unity" used, and see their examples.
In fact, I think you can just take any nonassociative ring $R$ and perform the standard Dorroh construction on $mathbb Ztimes R$ to get a nonassociative ring with identity.
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
$endgroup$
add a comment |
$begingroup$
Nobody said associativity was required.
You can search the web and find the phrase "nonassociative ring with unity" used, and see their examples.
In fact, I think you can just take any nonassociative ring $R$ and perform the standard Dorroh construction on $mathbb Ztimes R$ to get a nonassociative ring with identity.
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
$endgroup$
add a comment |
$begingroup$
Nobody said associativity was required.
You can search the web and find the phrase "nonassociative ring with unity" used, and see their examples.
In fact, I think you can just take any nonassociative ring $R$ and perform the standard Dorroh construction on $mathbb Ztimes R$ to get a nonassociative ring with identity.
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
$endgroup$
Nobody said associativity was required.
You can search the web and find the phrase "nonassociative ring with unity" used, and see their examples.
In fact, I think you can just take any nonassociative ring $R$ and perform the standard Dorroh construction on $mathbb Ztimes R$ to get a nonassociative ring with identity.
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
answered Dec 5 '18 at 15:03
rschwiebrschwieb
105k12100245
105k12100245
add a comment |
add a comment |
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