Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 1, pp. 211228 (2006) 

Generalized adjoint semigroups of a ringXiankun Du and Junlin WangDepartment of Mathematics, Jilin University, Changchun 130012, China; email: duxk@jlu.edu.cnAbstract: In this paper, we introduce generalized adjoint semigroups (GAsemigroups) of a ring $R$. We construct generalized adjoint semigroups on a ring $R$ by means of bitranslations of $R$. It is shown that GAsemigroups of a $\pi$regular ring are $\pi$regular. As an application we deduce that in any ring, idempotents can be lifted modulo $\pi$regular ideals. GAsemigroups containing idempotents are described in terms of the ring of a Morita context. Full text of the article:
Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.
© 2006 Heldermann Verlag
