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6.4.7. (a) Show that a subring R' of an integral domain R is an integral domain,...

6.4.7.
(a) Show that a subring R' of an integral domain R is an integral
domain, if 1∈ R'.
(b) The Gaussian integers are the complex numbers whose real and
imaginary parts are integers. Show that the set of Gaussian integers
is an integral domain.
(c) Show that the ring of symmetric polynomials in n variables is an
integral domain.

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