Vol. 97, No. 2, 1981

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Right chain rings and the generalized semigroup of divisibility

Hans-Heinrich Brungs and Günter Törner

Vol. 97 (1981), No. 2, 293–305
Abstract

Let R be a ring with unit element and without zero-divisors and let H(R) = {x|0x 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
Authors
Hans-Heinrich Brungs
Günter Törner