User talk:Richard L. Peterson
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Kind Regards,
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 in 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 in 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)