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As of definition, say, we have a and b non-zeros. If a*b = 0, then a and b are zero-divisors. | As of definition, say, we have a and b non-zeros. If a*b = 0, then a and b are zero-divisors. | ||
| − | I guess, the name zero-divisor comes from the same equation: 0/a = b. If you divide 0 by some non-zero element, you again get non-zero element. Well, our logic(intuition) of integers says differently: if any number divides 0 or multiplies with 0, the result will be 0 anyway. That is why we denote such concept of zero-divisors, so we could take them out and get closer to the model of integers abstractly. | + | I guess, the name zero-divisor comes from the same equation: 0/a = b. If you divide 0 by some non-zero element, you again get non-zero element. Well, our logic(intuition) of integers says differently: if any non-zero number divides 0 or multiplies with 0, the result will be 0 anyway. That is why we denote such concept of zero-divisors, so we could take them out and get closer to the model of integers abstractly. |
Otherwise, zero-divisors have a right to be. | Otherwise, zero-divisors have a right to be. | ||
--[[User:guteulin|Galymzhan]] April 21 2009 (UTC) | --[[User:guteulin|Galymzhan]] April 21 2009 (UTC) | ||
[[Category:MA453Spring2009Walther]] | [[Category:MA453Spring2009Walther]] | ||
Latest revision as of 14:31, 21 April 2009
Does anyone fully understand the definition of zero divisors? If anyone could explain the def. further I would appreciate it!
--Lmiddlet 22:22, 11 March 2009 (UTC)
Ok, it might be kind of late to respond, but still it might help.
As of definition, say, we have a and b non-zeros. If a*b = 0, then a and b are zero-divisors.
I guess, the name zero-divisor comes from the same equation: 0/a = b. If you divide 0 by some non-zero element, you again get non-zero element. Well, our logic(intuition) of integers says differently: if any non-zero number divides 0 or multiplies with 0, the result will be 0 anyway. That is why we denote such concept of zero-divisors, so we could take them out and get closer to the model of integers abstractly.
Otherwise, zero-divisors have a right to be. --Galymzhan April 21 2009 (UTC)
