New characterizations of commutative clean rings |
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| Author |
zabavskii@gmail.com, gatalevych@ukr.net
Department of Mechanics and Mathematics,
Ivan Franko National University of Lviv
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| Abstract |
A ring is called clean if every its element is the sum of a unit and an idempotent. We
introduce the notion of an avoidable element and describe class of the commutative clean rings
as the rings in which zero is an avoidable element.
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| Keywords |
Bezout ring; neat ring; clean ring; elementary divisor ring; stable range 1; neat range 1
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| DOI |
doi:10.15330/ms.44.2.115-118
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| Reference |
1. O. Helmer, The elementary divisor for rings without chain condition, Bull. Amer. Math. Soc., 49 (1943),
¹2, 235–236.
2. I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc., 66 (1949), 464–491. 3. M. Larsen, W. Lewis, T. Shores, Elemetary divisor rings and finitely presented modules, Trans. Amer. Mat. Soc., 187 (1974), 231–248. 4. W. McGovern, Neat rings, J. Pure Appl. Alg., 205 (2006), ¹2, 243–265. 5. W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Mat. Soc., 229 (1977), 269–279. |
| Pages |
115-118
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| Volume |
44
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| Issue |
2
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| Year |
2015
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |