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On periodic rings.

Du, Xiankun, Yi, Qi (2001)

International Journal of Mathematics and Mathematical Sciences

On rings with a unique proper essential right ideal

O. A. S. Karamzadeh, M. Motamedi, S. M. Shahrtash (2004)

Fundamenta Mathematicae

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 is Artin semisimple...

On S -Noetherian rings

Zhongkui Liu (2007)

Archivum Mathematicum

Let R be a commutative ring and S R a given multiplicative set. Let ( M , ) be a strictly ordered monoid satisfying the condition that 0 m for every m M . Then it is shown, under some additional conditions, that the generalized power series ring [ [ R M , ] ] is S -Noetherian if and only if R is S -Noetherian and M is finitely generated.

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