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Let R be a ring with the property that every element is either nilpotent or invertible. If a, b, c are in R with a and b nilpotent, show that ac, ca, and a + b are nilpotent. For the latter, first observe that a + b cannot equal 1. Conclude that Nil (R) is the set of all nilpotent elements of R.
(nil radical Nil (R) is defined to be the sum of all nil two-sided ideals of R)
Calculate the LCM
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Solve the equation by order of operations.
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we are all familiar with the concept of correlation. it is a powerful tool to help us see how strongly two variables
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