A short proof of a fibre criterion for polynomials to belong to an ideal.

Nowak, Krzysztof Jan

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A “class group” obstruction for the equation $C y^{d} = F (x, z)$

Denis Simon (2008)

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In this paper, we study equations of the form $C y^{d} = F (x, z)$ , where $F \in ℤ [x, z]$ is a binary form, homogeneous of degree $n$ , which is supposed to be primitive and irreducible, and $d$ is any fixed integer. Using classical tools in algebraic number theory, we prove that the existence of a proper solution for this equation implies the existence of an integral ideal of given norm in some order in a number field, and also the existence of a specific relation in the class group involving this ideal. In some cases,...

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Ali Akbar Estaji (2008)

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Let $C (X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C (X)$ . The intersection of essential weak ideal in $C (X)$ is also studied.