Let H be a Krull monoid with infinite class group such that each divisor class contains a prime divisor. We show that for every positive integer n, there exists a divisor closed submonoid S of H such that min∆(S) = n.

Let f(n) or the base-2 logarithm of f(n) be either d(n) (the divisor function), σ(n) (the divisor-sum function), φ(n) (the Euler totient function), ω(n) (the number of distinct prime factors of n) or Ω(n) (the total number of prime factors of n). We present good lower bounds for ∣ ∣M N − α ∣ ∣ in terms of N , where α = [0; f(1), f(2), . . .].

We announce some new results about systems of residue sets. A residue set R C Z is an arithmetic progression R = {a,a±n,a± 2n,...}. The positive integer n is referred to as the modulus of R. Following Znam [21] we denote this set by a(n). We need several number-theoretic functions. p(ra)-the least prime divisor of a natural number ra, P(m)-the greatest prime divisor of ra, A(m)-the greatest div...

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.

Let E be an elliptic curve defined over Q. For any prime p of good reduction, let Ep be the reduction of E mod p. Denote by Np the cardinality of Ep(Fp), where Fp is the finite field of p elements. Let P (Np) be the greatest prime divisor of Np. We prove that if E has CM then for all but o(x/ log x) of primes p ≤ x, P (Np) > p, where θ(p) is any function of p such that θ(p)→ 0 as p→∞. Moreover ...

If S is a Krull monoid with finitely generated divisor class group such that only finitely many divisor classes of S contain prime divisors, then we construct an algorithm to compute the elasticity of S. © 2001 Elsevier Science Inc. All rights reserved. AMS classification: 20M14; 20M25; 13F05; 11Y05

orbit closure, 32 character, 33cone, 9dual, 10lattice, 10strongly convex, 10convex function, 42 distinguished point, 28divisorCartier, 38T -invariant, 40principal, 39prime, 37Weil, 37T -invariant, 39principal, 38divisor class group, 38

This paper investigates cross correlation properties of sequences derived from GH sequences modulo p, where p is a prime number and presents comparison with cross correlation properties of pseudo noise sequences. For GH sequences modulo prime, a binary random sequence B(n) is constructed, based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). We show that B(n) sequences have ...

Almost 20 years ago, W. Narkiewicz posed the problem to give an arithmetical characterization of the ideal class group of an algebraic number field ([13, problem 32]). In the meantime there are various answers to this question if the ideal class group has a special form. (cf. [4], [5], [12] and the literature cited there). The general case was treated by J. Koczorowski [11], F. Halter-Koch [8],...