On rings of integers generated by their units

Stable Rings Generated by Their Units

We introduce the class of rings satisfying (m,1)-stable range and investigate equivalent characterizations of such rings. These give generalizations of the corresponding results by Badawi (1994), Ehrlich (1976), and Fisher and Snider (1976). 2000 Mathematics Subject Classification. 19B10, 16E50. Let R be an associative ring with identity. A ring R is said to have stable range one provided that ...

Groups generated by two bicyclic units in integral group rings

Rings of Integers, Gauss-jacobi Sums, and Their Applications

In this paper we shall explore the structure of the ring of algebraic integers in any quadratic extension of the field of rational numbers Q, develop the concepts of Gauss and Jacobi sums, and apply the theory of algebraic integers and that of Gauss-Jacobi sums to solving problems involving power congruences and power sums as well as to proving the quadratic and cubic reciprocity laws. In parti...

On Sequences of Integers Generated by a Sievin G Process

0 . Introduction The Sieve of Erathostenes is an algorithm which yields the sequence of all primes . This paper deals with a family of somewhat similar algorithm s for creating sequences of integers . These algorithms depend on an initial integer 2 and on an auxilary sequence B of integers b k (k = 1, 2, . . .) with b k > 2 . A family of intermediary sequences Xi ) (i = 1, 2, . . .) is formed, ...

On Semigroups Generated by Two Consecutive Integers and Hermitian Codes

Analysis of the Berlekamp-Massey-Sakata algorithm for decoding onepoint codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks that may be recovered by their majority voting algorithm. The second method is to design the code to correct only those error vectors of a given weight that are also geometrically generic. In this work, formulae are gi...