Right chain rings and the generalized semigroup of divisibility

Hans-Heinrich Brungs and Günter Törner

Vol. 97 (1981), No. 2, 293–305

DOI: 10.2140/pjm.1981.97.293

Abstract

Let R be a ring with unit element and without zero-divisors and let H(R) = {x|0≠x ∈ R} where x is the mapping from the set of all nonzero principal right ideals of R into itself defined by x(aR) = xaR. H(R) is a partially ordered semigroup that can be considered as a generalization of the group of divisibility of a commutative integral domain. We study those rings R for which H(R) is totally ordered.

Mathematical Subject Classification 2000

Primary: 16A15, 16A15

Secondary: 06F05, 16A02

Milestones

Received: 2 September 1979

Published: 1 December 1981