Is multiplicative identity of a commutative and idempptent semiring always additively absorbing?
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It is easy to see with the counter examples that multiplicative identity $e$ of a commutative ( $xy=yx~forall~x,yin R$) and multiplicatively idempptent ($xx=x~forall~xin R$) semiring $R$ is additively absorbing too. But i think in general the answer is $bf No$.
semiring
asked Dec 15 '18 at 9:43
getegete
847
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It is easy to see with the counter examples that multiplicative identity $e$ of a commutative ( $xy=yx~forall~x,yin R$) and multiplicatively idempptent ($xx=x~forall~xin R$) semiring $R$ is additively absorbing too. But i think in general the answer is $bf No$.
semiring
asked Dec 15 '18 at 9:43
getegete
847
$endgroup$
add a comment |
$begingroup$
It is easy to see with the counter examples that multiplicative identity $e$ of a commutative ( $xy=yx~forall~x,yin R$) and multiplicatively idempptent ($xx=x~forall~xin R$) semiring $R$ is additively absorbing too. But i think in general the answer is $bf No$.
semiring
asked Dec 15 '18 at 9:43
getegete
847
$endgroup$
It is easy to see with the counter examples that multiplicative identity $e$ of a commutative ( $xy=yx~forall~x,yin R$) and multiplicatively idempptent ($xx=x~forall~xin R$) semiring $R$ is additively absorbing too. But i think in general the answer is $bf No$.
semiring
semiring
asked Dec 15 '18 at 9:43
getegete
847
asked Dec 15 '18 at 9:43
getegete
847
asked Dec 15 '18 at 9:43
getegete
847
asked Dec 15 '18 at 9:43
getegete
847
asked Dec 15 '18 at 9:43
getegete
847
847
add a comment |
add a comment |
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