Very Decomposable Abelian Groups.
Martin Ziegler, Rüdiger Göbel (1988/89)
Mathematische Zeitschrift
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Martin Ziegler, Rüdiger Göbel (1988/89)
Mathematische Zeitschrift
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Junchao Wei (2013)
Communications in Mathematics
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A ring is defined to be left almost Abelian if implies for and , where and stand respectively for the set of idempotents and the set of nilpotents of . Some characterizations and properties of such rings are included. It follows that if is a left almost Abelian ring, then is -regular if and only if is an ideal of and is regular. Moreover it is proved that (1) is an Abelian ring if and only if is a left almost Abelian left idempotent reflexive ring. (2) ...
Manfred Dugas, Rüdiger Göbel (1982)
Mathematische Annalen
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C. Calderón (2003)
Publications de l'Institut Mathématique
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Kenneth K. Nwabueze (1997)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Brendan Goldsmith, Peter Vámos (2007)
Rendiconti del Seminario Matematico della Università di Padova
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Anne C. Morel (1968)
Colloquium Mathematicae
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Fred Clare (1976)
Colloquium Mathematicae
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Krzysztof Krupiński (2005)
Fundamenta Mathematicae
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Kharazishvili, Aleksander (2015-11-18T12:34:03Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Feigelstock, Shalom (1983-1984)
Portugaliae mathematica
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Mateusz Woronowicz (2016)
Annales Mathematicae Silesianae
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Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.