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Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

1 vote
0 answers
118 views

Translation of a paper by Dedekind (an integral basis for pure cubic fields)

I am studying Introductory Algebraic Number Theory written by S. Alaca and K. Williams. The authors mention the theorem concerning an integral basis for pure cubic fields but do not provide proof. How …
Infinity_hunter's user avatar
3 votes
1 answer
253 views

Do there exist irreducible elements in this domain?

I asked this question on MSE. Here also I have the same motive in the question. Let $D= \{\,a_1x^{r_1} + \cdots + a_n x^{r_n} \, \vert \, a_i \in \mathbb{C} \text{ for } i= 1,2,\dots,n \text{ and eac …
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