Question
Let . Check whether D is a UFD or not.
Answer :
Word Count : 120
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Observe that (D={f(x,y)+g(x,y)i \mid f,g\in \mathbb Z[x,y]}) can be written as (D=\mathbb Z[i][x,y]), since every element has coefficients in the Gaussian integers (\mathbb Z[i]), and conversely every polynomial
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दर्शाइए कि R/M एक क्षेत्र है, तथा इस क्षेत्र के दो अलग-अलग शून्येतर अवयव दीजिए।
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मान लीजिए कि R एक क्रमविनिमेय तत्समकी वलय है और . समाकारिता के मूल प्रमेय का प्रयोग करते हुए, सिद्ध कीजिए कि
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इस तरह, दर्शाइए कि
Let G be a group such that is cyclic. Prove that G is abelian.
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अतः, दर्शाइए कि यदि N, R की एक ऐसी गुणजावली है जिसका M एक उचित
सिद्ध कीजिए कि (n बार)
और
.