Integral domain $0$ element

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An integral domain is defined as a commutative ring with 1 that it's elements comply
$x*y=0 Rightarrow x=0 $ or $y=0$



Is this element $0$ the one of $Bbb Z$ or is the neutral element of the set we are working in such ring.




ring-theory field-theory integral-domain




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    An integral domain is defined as a commutative ring with 1 that it's elements comply
    $x*y=0 Rightarrow x=0 $ or $y=0$



    Is this element $0$ the one of $Bbb Z$ or is the neutral element of the set we are working in such ring.




    ring-theory field-theory integral-domain




    share|cite|improve this question





















      up vote
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      down vote

      favorite









      up vote
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      down vote

      favorite











      An integral domain is defined as a commutative ring with 1 that it's elements comply
      $x*y=0 Rightarrow x=0 $ or $y=0$



      Is this element $0$ the one of $Bbb Z$ or is the neutral element of the set we are working in such ring.




      ring-theory field-theory integral-domain




      share|cite|improve this question











      An integral domain is defined as a commutative ring with 1 that it's elements comply
      $x*y=0 Rightarrow x=0 $ or $y=0$



      Is this element $0$ the one of $Bbb Z$ or is the neutral element of the set we are working in such ring.





      ring-theory field-theory integral-domain





      share|cite|improve this question










      share|cite|improve this question




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      asked Jul 17 at 23:37









      Jorge

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          The latter: unless the ring is itself the integers, 0 will mean that ring's additive identity rather than the natural number 0.



          And anyways, multiplication is a binary operation $R times R to R$, so unless 0 is an element of the ring, it won't be the product of two elements.






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            The latter: unless the ring is itself the integers, 0 will mean that ring's additive identity rather than the natural number 0.



            And anyways, multiplication is a binary operation $R times R to R$, so unless 0 is an element of the ring, it won't be the product of two elements.






            share|cite|improve this answer

























              up vote
              2
              down vote













              The latter: unless the ring is itself the integers, 0 will mean that ring's additive identity rather than the natural number 0.



              And anyways, multiplication is a binary operation $R times R to R$, so unless 0 is an element of the ring, it won't be the product of two elements.






              share|cite|improve this answer























                up vote
                2
                down vote










                up vote
                2
                down vote









                The latter: unless the ring is itself the integers, 0 will mean that ring's additive identity rather than the natural number 0.



                And anyways, multiplication is a binary operation $R times R to R$, so unless 0 is an element of the ring, it won't be the product of two elements.






                share|cite|improve this answer













                The latter: unless the ring is itself the integers, 0 will mean that ring's additive identity rather than the natural number 0.



                And anyways, multiplication is a binary operation $R times R to R$, so unless 0 is an element of the ring, it won't be the product of two elements.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 17 at 23:41









                Spencer

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