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Ring of integers
About: Ring of integers is a research topic. Over the lifetime, 1856 publications have been published within this topic receiving 15882 citations.
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TL;DR: In this paper, it was shown that cancellation of finitely generated torsion-free R-modules is valid if and only if every unit of O /c O is liftable to a unit of ǫ O.
3 citations
TL;DR: In this paper, a complete list of representatives of conjugacy classes of torsion in the 4 A 4 general linear group over ring of integers is given, with 45 distinct classes, each having order 1, 2, 3, 4, 5, 6, 8, 10 or 12.
Abstract: The problem of integral similarity of block-triangular matrices over the ring of integers is connected to that of finding representatives of the classes of an equivalence relation on general integer matrices. A complete list of representatives of conjugacy classes of torsion in the 4 A 4 general linear group over ring of integers is given. There are 45 distinct such classes and each torsion element has order of 1, 2, 3, 4, 5, 6, 8, 10 or 12.
3 citations
TL;DR: In this article, the authors prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers, and prove a similar formula for the local height on a circle of integers.
Abstract: In this short note we prove a formula for local heights on elliptic curves over number fields in terms of intersection theory on a regular model over the ring of integers.
3 citations
TL;DR: In this paper, it was shown that every integer of a cyclic Galois extension of a number field with zero trace is a difference of two conjugates if and only if there is an integer of E with trace 1.
3 citations
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TL;DR: In this article, it was shown that there are infinitely many non-Wieferich primes with respect to certain units in the ring of integers under the assumption of the \textit{abc} conjecture for number fields.
Abstract: Let $K/\mathbb{Q}$ be an algebraic number field of class number one and $\mathcal{O}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in $\mathcal{O}_K$ under the assumption of the \textit{abc} conjecture for number fields.
3 citations