Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 211-228 (2006)
Generalized adjoint semigroups of a ring
Xiankun Du and Junlin WangDepartment of Mathematics, Jilin University, Changchun 130012, China; e-mail: firstname.lastname@example.org
Abstract: In this paper, we introduce generalized adjoint semigroups (GA-semigroups) of a ring $R$. We construct generalized adjoint semigroups on a ring $R$ by means of bitranslations of $R$. It is shown that GA-semigroups 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. GA-semigroups containing idempotents are described in terms of the ring of a Morita context.
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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.