Find all the units of .
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Prove that a cyclic group with only one generator can have at most 2 elements.
क) क्रमविनिमेय वलय R की गुणजावली I के लिए,, किसी
के लिए परिभाषित कीजिए। दिखाइए कि
यहाँ चित्र में दिए गए टेक्स्ट का लिखित रूप है:
i) की एक गुणजावली है।
ii) .
iii) कुछ स्थितियों में
।
ख) क्या वलय R की कोई भी दो गुणजावलियों I और J के लिए,
? अपने
उत्तर की पुष्टि कीजिए।
(5)
Find all the units of .
Check whether or not
is a field.
Is , for any two ideals I and J of a ring R? Give reasons for your answer.
Let be a fixed odd permutation in S10. Show that every odd permutation in S10 is a product of
and some permutation in A10.
या H अपरिमित है;
Prove that every non-trivial subgroup of a cyclic group has finite index. Hence prove that is not cyclic.