A categorical contribution to the Kummer theory of ideal numbers
A certain property of polynomials.
A certain property of polynomials. (Short Communication).
A Characterization of Algebraic Number Fields with Cyclic Class Group of Prime Power Order.
A complete generalization of Yokoi's p-invariants
A congruence for the index of a unit of a real abelian number field
A Cuspidal Class Number Formula for the Modular Curves X1(N).
A generalization of a unit index of Greither
A generalization of Davenport's constant and its arithmetical applications
A generalization of Dirichlet's unit theorem
We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence...
A “Hardy-Littlewood” approach to the -unit equation
A note on a cyclotomic diophantine equation
A note on certain semigroups of algebraic numbers
The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ ℤ, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic(divisor theory) and analytic(distribution of elements with a given norm) properties of that semigroup and a related semigroup of ideals....
A note on circular distributions
A note on circular units in -extensions
In this note we consider projective limits of Sinnott and Washington groups of circular units in the cyclotomic -extension of an abelian field. A concrete example is given to show that these two limits do not coincide in general.
A Note on Cyclotomic Fields.
A note on global units and local units of function fields
A note on numbers with good factorization properties
A note on Sinnott's index formula
Let k be an (imaginary or real) abelian number field whose conductor has two distinct prime divisors. We shall construct a basis for the group C of circular units in k and compute the index of C in the group E of units in k. This result is a generalization of Theorem 3.3 in a previous paper [1].
A Note on Subsemigroups with Divisor Theory.