User talk:Richard L. Peterson: Difference between revisions
imported>Sébastien Moulin m (typo) |
imported>Sébastien Moulin m (→Zero being a divisor: typo) |
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Hi Richard, | Hi Richard, | ||
I modified a little the article [[divisor]] and tried to explain my changes | I modified a little the article [[divisor]] and tried to explain my changes on the [[Talk:divisor]] page, but unfortunately it didn't work (there seems to be a bug preventing me of creating this talk page). Here is the explanation I intented to put on the talk page. | ||
My textbooks do not require a divisor to be non zero : I usually read that in a -- say commutative -- [[ring (mathematics)|ring]], ''d'' is a divisor of ''a'' if there is a ''k'' such that ''a=kd'', whithout any other requirement. I suppose some authors may exclude the case ''d=0'' to avoid to define the quotient ''0/0''. I made some changes in the articles in this sense. On the other side, it is true that ''d=0'' is excluded when one wants to define a "divisor of zero" in any ring, and then define an [[integral domain]] as a ring without divisors of zero; but anyway, here, "divisor of zero" is a slightly different thing, because it is required this time that ''k'' is non zero (else any element of any ring would be a divisor of zero). | My textbooks do not require a divisor to be non zero : I usually read that in a -- say commutative -- [[ring (mathematics)|ring]], ''d'' is a divisor of ''a'' if there is a ''k'' such that ''a=kd'', whithout any other requirement. I suppose some authors may exclude the case ''d=0'' to avoid to define the quotient ''0/0''. I made some changes in the articles in this sense. On the other side, it is true that ''d=0'' is excluded when one wants to define a "divisor of zero" in any ring, and then define an [[integral domain]] as a ring without divisors of zero; but anyway, here, "divisor of zero" is a slightly different thing, because it is required this time that ''k'' is non zero (else any element of any ring would be a divisor of zero). | ||
Feel free to comment on it and to edit this article again if needed. Best regards, --[[User:Sébastien_Moulin|Sébastien Moulin]] <small>[[User_talk:Sébastien_Moulin|(talk me)]]</small> 05:28, 31 March 2007 (CDT) | Feel free to comment on it and to edit this article again if needed. Best regards, --[[User:Sébastien_Moulin|Sébastien Moulin]] <small>[[User_talk:Sébastien_Moulin|(talk me)]]</small> 05:28, 31 March 2007 (CDT) | ||
Revision as of 07:01, 31 March 2007
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Robert Tito | Talk 10:50, 29 March 2007 (CDT)
Zero being a divisor
Hi Richard, I modified a little the article divisor and tried to explain my changes on the Talk:divisor page, but unfortunately it didn't work (there seems to be a bug preventing me of creating this talk page). Here is the explanation I intented to put on the talk page.
My textbooks do not require a divisor to be non zero : I usually read that in a -- say commutative -- ring, d is a divisor of a if there is a k such that a=kd, whithout any other requirement. I suppose some authors may exclude the case d=0 to avoid to define the quotient 0/0. I made some changes in the articles in this sense. On the other side, it is true that d=0 is excluded when one wants to define a "divisor of zero" in any ring, and then define an integral domain as a ring without divisors of zero; but anyway, here, "divisor of zero" is a slightly different thing, because it is required this time that k is non zero (else any element of any ring would be a divisor of zero).
Feel free to comment on it and to edit this article again if needed. Best regards, --Sébastien Moulin (talk me) 05:28, 31 March 2007 (CDT)