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Two questions on semi-clean group rings

Institution:	1. The Ohio State University at Lima, Lima, OH, USA;2. Università di Camerino, Camerino, Italy;1. Centro marplatense de Investigaciones Matemáticas, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata, 7600 Mar del Plata, Argentina;2. CONICET, Argentina;1. Department of Mathematics, Miami Dade College, Miami, FL 33135, United States of America;2. Department of Mathematics, MIT, Cambridge, MA 02139, United States of America;1. Department of Mathematics, Swansea University, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK;2. Faculty of Mathematics, University of Bia?ystok, K. Cio?kowskiego 1M, 15-245 Bia?ystok, Poland;3. Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK;4. Département de Mathématique, Université Libre de Bruxelles, Bd du Triomphe, B-1050 Brussels, Belgium;1. School of Mathematics and Statistics, University of New South Wales, UNSW, Sydney 2052, Australia;2. MIIT Key Laboratory of Mathematical Theory and Computation in Information Security, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, PR China

Abstract:	It was proved in 4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in 4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.

Keywords:	Local ring Clean ring Weakly clean ring Semi-clean ring Torsion abelian group Group ring
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