-clean rings.
Chen, Weixing (2006)
International Journal of Mathematics and Mathematical Sciences
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Chen, Weixing (2006)
International Journal of Mathematics and Mathematical Sciences
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Bakkari, Chahrazade, Mahdou, Najib (2009)
Beiträge zur Algebra und Geometrie
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O. A. S. Karamzadeh, M. Motamedi, S. M. Shahrtash (2004)
Fundamenta Mathematicae
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Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and...
Lăcrimioara Iancu, Maria S. Pop (2000)
Discussiones Mathematicae - General Algebra and Applications
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We give a construction for (m,n)-rings of quotients of a semicommutative (m,n)-ring, which generalizes the ones given by Crombez and Timm and by Paunić for the commutative case. We also study various constructions involving reduced rings and rings of quotients and give some functorial interpretations.
Manfred Dugas, Shalom Feigelstock (2004)
Rendiconti del Seminario Matematico della Università di Padova
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Guo, Xiaojiang, Shum, K.P. (2006)
International Journal of Mathematics and Mathematical Sciences
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Khazal, R., Dăscălescu, S., Van Wyk, L. (2003)
International Journal of Mathematics and Mathematical Sciences
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Huanyin Chen, Fu-An Li (2002)
Collectanea Mathematica
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In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.
Eliza Wajch (1988)
Colloquium Mathematicae
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Manfred Dugas, Shalom Feigelstock (2003)
Colloquium Mathematicae
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A ring R is called an E-ring if every endomorphism of R⁺, the additive group of R, is multiplication on the left by an element of R. This is a well known notion in the theory of abelian groups. We want to change the "E" as in endomorphisms to an "A" as in automorphisms: We define a ring to be an A-ring if every automorphism of R⁺ is multiplication on the left by some element of R. We show that many torsion-free finite rank (tffr) A-rings are actually E-rings. While we have an example...
Heatherly, H.E., Courville, J.R. (1999)
Mathematica Pannonica
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Khan, Moharram A. (2000)
International Journal of Mathematics and Mathematical Sciences
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Robert Yue Chi Ming (1979)
Monatshefte für Mathematik
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Bell, Howard E., Klein, Abraham A. (2002)
International Journal of Mathematics and Mathematical Sciences
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Piotr Jędrzejewicz (2011)
Colloquium Mathematicae
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We observe that the characterization of rings of constants of derivations in characteristic zero as algebraically closed subrings also holds in positive characteristic after some natural adaptation. We also present a characterization of such rings in terms of maximality in some families of rings.