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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
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Is there a cyclic structure in rings?
Is group theory we have defined order of an element and hence we have seen the existence of cyclic structure... can we have that in rings as well?? if not, why?
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Priyadarshan Choursiya![best-answer]()
ring with squarefree order is a cyclic ring. Every subring of a cyclic ring is a cyclic ring. Moreover, every subring of a cyclic ring is an ideal. A number is said to be square free if no prime factor divides it more than once, i.e., largest power of a prime factor that divides n is one. First few square free numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, see attachment