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Please give examples for (a) a non-commutative ring (b) a subgroup H of a group G...

Please give examples for
(a) a non-commutative ring

(b) a subgroup H of a group G which is not normal in G
(c) a commutative ring R in which the zero ideal {0} is not prime

(d) a nonzero proper ideal J in a commutative ring IZ which is not maximal in R

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