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P. V´amos called a ring R 2-good if every element is the sum of two units. The ring of all n × n matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2- good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if R is an exchange ring with Artinian primitive factors and 2 is a unit in R, then R is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.
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참고문헌 (24)
참고문헌 신청
A. A. Tuganbaev / 2002 / Rings and modules with exchange properties / J. Math. Sci 110 (1) : 2348 ~ 2421
A. Badawi / 1994 / On semicommutative π-regular rings / Comm. Algebra 22 (1) : 151 ~ 157
A. Badawi / 1997 / On abelian π-regular rings / Comm. Algebra 25 (4) : 1009 ~ 1021
A. V. Kelarev / 2002 / Ring Constructions and Applications / World Scientific
B. Zimmermann-Huisgen / 1984 / Classes of modules with the exchange property / J. Algebra 88 (2) : 416 ~ 434
A. Badawi / 1994 / On semicommutative π-regular rings / Comm. Algebra 22 (1) : 151 ~ 157
A. Badawi / 1997 / On abelian π-regular rings / Comm. Algebra 25 (4) : 1009 ~ 1021
A. V. Kelarev / 2002 / Ring Constructions and Applications / World Scientific
B. Zimmermann-Huisgen / 1984 / Classes of modules with the exchange property / J. Algebra 88 (2) : 416 ~ 434
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