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Suppose that R is a commutative ring without zero-divisors. Let x and y be nonzero elements....

Suppose that R is a commutative ring without zero-divisors.
Let x and y be nonzero elements.
1. Suppose that x has infinite additive order.
Show that y also has infinite additive order.


2. Suppose that the additive order of x is n.
Show that the additive order of y is at most n.


3.Show that all the nonzero elements of R have the same additive order.

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