Journal ArticleDOI
Elementary and analytic theory of algebraic numbers (3rd edn), by W. Narkiewicz. Pp. 708. £92.50. 2004. ISBN 3 540 21902 1 (Springer).
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This article is published in The Mathematical Gazette.The article was published on 2005-07-01. It has received 18 citations till now. The article focuses on the topics: Algebraic number.read more
Citations
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The structure of blocks with a Klein four defect group
TL;DR: In this article, the authors prove Erdmann's conjecture that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig's finiteness conjecture holds for source algebras of blocks with a k-four defect group.
Journal ArticleDOI
On minimal distances in Krull monoids with infinite class group
TL;DR: In this article, it was shown that for every positive integer n, there exists a divisor closed submonoid S of H such that min Δ(S) = n.
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Comments on the height reducing property
Shigeki Akiyama,Toufik Zaïmi +1 more
TL;DR: In this article, a complex number alpha is said to satisfy the height reducing property if there is a finite subset F of the ring Z of the rational integers such that Z[alpha]=F[alpha].
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Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling
TL;DR: In this article, the authors considered the oscillation properties of the remainder term of the Beurling zeta function and its relation to the distribution of the nontrivial zeroes of the function.
Journal ArticleDOI
On relations for rings generated by algebraic numbers and their conjugates
TL;DR: In this paper, it was shown that a rational number (r/t) belongs to the ring of conjugate algebraic numbers over cubic algebraic integers if and only if the square-free part of its denominator (r, t) divides all the coefficients of the minimal polynomial (F \in \mathbb {Z}[X] ) except for a constant coefficient that must be relatively prime to r/t, namely (Gcd (F(0),t)=1).
References
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Journal ArticleDOI
The structure of blocks with a Klein four defect group
TL;DR: In this article, the authors prove Erdmann's conjecture that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig's finiteness conjecture holds for source algebras of blocks with a k-four defect group.
Journal ArticleDOI
Comments on the height reducing property
Shigeki Akiyama,Toufik Zaïmi +1 more
TL;DR: In this article, it was shown that a complex number satisfying the height reducing property is an algebraic number whose conjugates, over the field of the rationals, are all modulus one, or all of modulus greater than one.
Posted Content
Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling
TL;DR: In this article, the authors considered the oscillation properties of the remainder term of the Beurling zeta function and its relation to the distribution of the nontrivial zeroes of the function.
Journal ArticleDOI
On relations for rings generated by algebraic numbers and their conjugates
TL;DR: In this paper, it was shown that a rational number (r/t) belongs to the ring of conjugate algebraic numbers over cubic algebraic integers if and only if the square-free part of its denominator (r, t) divides all the coefficients of the minimal polynomial (F \in \mathbb {Z}[X] ) except for a constant coefficient that must be relatively prime to r/t, namely (Gcd (F(0),t)=1).
Journal ArticleDOI
Ternary quadratic forms and the class numbers of imaginary quadratic fields
Lei Gao,Hourong Qin +1 more
TL;DR: In this paper, a series of relations between the numbers of solutions of some positive definite ternary quadratic forms and the class numbers of corresponding imaginary quadrastic fields are established.