Abstract
It is proved that if R is a commutative ring in which zero is an adequate element, then R is an exchange ring and every zero adequate ring is an exchange ring. There is a new description of adequate rings; this is an answer to questions formulated by Larsen, Lewis, and Shores.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 3, pp. 61–66, 2011/12.
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Zabavsky, B.V., Bilavska, S.I. Every zero adequate ring is an exchange ring. J Math Sci 187, 153–156 (2012). https://doi.org/10.1007/s10958-012-1058-y
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DOI: https://doi.org/10.1007/s10958-012-1058-y