The unit sum number of Baer rings

Document Type : Other

Authors

1 Semnan UniversityFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.

2 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.

Abstract

In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of $R$ is isomorphic
to $Z_2$ and we characterize regular Baer rings with unit sum numbers $\omega$ and $\infty$. Then as an application, we discuss the unit  sum number of some classes of group rings.

Keywords

Main Subjects

References

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History

• Receive Date: 04 November 2013
• Revise Date: 10 February 2015
• Accept Date: 10 February 2015