Abstract Let $ K=\mathbb Q (\theta) $ be an algebraic number field with $\theta $ a root of an
irreducible polynomial $ f (x)= x^ 8+ ax^ m+ b\in\mathbb Z [x] $ and $1\leq m\leq 7$. We …

Let K be a number field with the ring of integers R and L= K (α). In this work, we give
necessary and sufficient conditions on a, b, s, n so that the irreducible polynomial P (X)= X …

Let $ L= K (\alpha) $ be an extension of a number field $ K $, where $\alpha $ satisfies the
monic irreducible polynomial $ P (X)= X^{p}-\beta $ of prime degree belonging to $\mathfrak …

Let K be a number field and L= K (α) where α satisfies the monic irreducible polynomial P
(X)= X3n− β in OK [X](OK is the ring of integer of K). In this paper we characterize the …

Let K be a number field with ring of integers R and L= K (α) where α satisfies the irreducible
polynomial P (X)= X 3 n+ a X 3 s− b of R [X](n, s∈ ℕ, n> s). We give necessary and sufficient …

Let $ K=\mathbb {Q}(\alpha) $ be a pure number field generated by $\alpha $ a root of a
monic irreducible polynomial $ F (x)\,=\, x^{3^ r\cdot 5^ s\cdot 7^ t}-m\in\mathbb {Z}[x] …

In this paper, we are going to exploit the irreducibility of the composite polynomial defined
on the same field to prove a New and useful result linking the index-ideal in Tower …

The theory of elliptic curves is distinguished by its diversity of the methods that have been
used in its study. The idea to examine and make sense to elliptic curve over a local …

Let K be a number field and L= K (α) where α satisfies the monic irreducible polynomial P
(X)= Xpn− β in OK [X](OK is the ring of integer of K). In this paper we characterize the …