Adequate properties of elements in Abelian and duo-rings
نویسندگان
چکیده
منابع مشابه
Quasi-Duo Rings and Stable Range Descent
In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. ...
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15 صفحه اولDivisibility Properties of Group Rings over Torsion-free Abelian Groups
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15 صفحه اولTwo-Sided Properties of Elements in Exchange Rings
For any element a in an exchange ring R, we show that there is an idempotent e ∈ aR ∩ Ra such that 1 − e ∈ (1 − a)R ∩ R (1 − a). A closely related result is that a ring R is an exchange ring if and only if, for every a ∈ R, there exists an idempotent e ∈ Ra such that 1− e ∈ (1−a)R. The Main Theorem of this paper is a general two-sided statement on exchange elements in arbitrary rings which subs...
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ژورنال
عنوان ژورنال: Prykladni Problemy Mekhaniky i Matematyky
سال: 2019
ISSN: 1810-3022
DOI: 10.15407/apmm2019.17.47-50