Consider { 0,2,4} as a subset of Z6 . show it is a subring. does it have unity?
Let us consider as a subset of . Let us show that is a subring of Since 0-0=0\in\Z_6,\ 2-0=2\in\Z_6,\ 4-0=4\in\Z_6,\ 0-2=4\in\Z_6,\ 2-2=0\in\Z_6,\ 4-2=2\in\Z_6,\ 0-4=2\in\Z_6,\ 2-4=4\in\Z_6,\ 4-4=0\in\Z_6,\
we conclude that the operation of substraction is closed on
Taking into account that and we conclude that the operation of multiplication is closed on
Therefore, is a subring of
Taking into account that we conclude that is unity of
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