Displaying similar documents to “A Note On A Class Of Noetherian Rings”

Reduced near-rings

Szeto, George, Wong, Yuen-Fat (1981)

Portugaliae mathematica

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S V -Rings and S V -Porings

Niels Schwartz (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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S V -rings are commutative rings whose factor rings modulo prime ideals are valuation rings. S V -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of S V -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered S V -rings ( S V -porings)...

On rings with a unique proper essential right ideal

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...