Solutions to your How to Problems

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1. What is the cardinality of the set of the subrings of Q?
Solution


2. In a finite ring R, show that there exist two distinct positive integers m,n such that for every x in R, x^m=x^n.
Solution


3. In a ring R, show that if an element x has two distinct right inverses, then it has infinitely many of them.
Solution



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