user46220

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22 Questions

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10	Solve $y^2= x^3 − 33$ in integers
3	Show that the equation $y^2 = x^3 + 7$ has no integral solutions.
2	Use Nakayama's Lemma to show that $I$ is principal, generated by an idempotent. [duplicate]
1	Show if the elements of $B$ are integral and $\Delta_{B}(K)$ is square-free, then $\mathcal{O}_K = \mathbb{Z}b_1 + \cdots + \mathbb{Z}b_d$. [duplicate]
1	Show that the $\mathbb{Z}$-span $\mathbb{Z}b'_1+\cdots+ \mathbb{Z}b'_d$ of $B^+$ does not depend on the choice of $B$

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136 Reputation

+5	Use Nakayama's Lemma to show that $I$ is principal, generated by an idempotent.
+53	Solve $y^2= x^3 − 33$ in integers
+5	Show that if both $M'$,$M''$ are finitely generated then so is $M$
+5	Show that $P[X]$ is a prime ideal of $R[X]$

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10 Tags

0 abstract-algebra × 10	0 discrete-mathematics × 3
0 algebraic-number-theory × 8	0 combinatorics × 3
0 number-theory × 8	0 diophantine-equations × 2
0 commutative-algebra × 4	0 p-adic-number-theory
0 elementary-number-theory × 3	0 field-theory

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Mathematics

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