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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 article, it was shown that σ* is of weak type (1, 1) on Hardy-Lorentz spaces, where σ ∈ L1( O ).
4 citations
TL;DR: It was shown in this paper that there are infinitely many quadratic extensions of rational functions in one variable over finite prime fields such that the ring of integers is a unique factorization domain.
4 citations
TL;DR: In this paper, the authors study the case in which finitely generated ideals of polynomials are uniquely determined by their ideals of values at each element of a noetherian domain.
Abstract: Let B be the ring of integral valued polynomials over a noetherian domain A. We study in which case finitely generated ideals of B are uniquely determined by their ideals of values at each element of A. We give necessary and sufficient conditions which are verified for example when A is any ring of integers of an algebraic number field, such that each quotient ring Am with respect to a maximal ideal m is analytically irreducible.
4 citations
TL;DR: In this article, the exceptional components in the Wedderburn decomposition of finite groups are divided into two types: type 1 are division rings, type 2 are $2 \times 2$-matrix rings.
Abstract: When considering the unit group of $\mathcal{O}_F G$ ($\mathcal{O}_F$ the ring of integers of an abelian number field $F$ and a finite group $G$) certain components in the Wedderburn decomposition of $FG$ cause problems for known generic constructions of units; these components are called exceptional. Exceptional components are divided into two types: type 1 are division rings, type 2 are $2 \times 2$-matrix rings. For exceptional components of type 1 we provide infinite classes of division rings by describing the seven cases of minimal groups (w.r.t. quotients) having those division rings in their Wedderburn decomposition over $F$. We also classify the exceptional components of type 2 appearing in group algebras of a finite group over number fields $F$ by describing all 58 finite groups $G$ having a faithful exceptional Wedderburn component of this type in $FG$.
4 citations
TL;DR: The idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain is refined and many new non-existence results for near BH matrices and near conference matrices are derived.
Abstract: In this paper we study the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson–Hadamard (BH) matrices and (near) conference matrices. We refine the idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain and get many new non-existence results for near BH matrices and near conference matrices. We also apply previous results on vanishing sums of roots of unity and self conjugacy condition to derive non-existence results for near BH matrices and near conference matrices.
4 citations