Displaying similar documents to “On pure semisimplicity and representation-finite piecewise prime rings”

A Unified approach to the Structure Theory of PI-Rings and GPI-Rings

Brešar, Matej (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 16R20, 16R50, 16R60, 16N60. We give short proofs, based only on basic properties of the extended centroid of a prime ring, of Martindale’s theorem on prime GPI-rings and (a strengthened version of) Posner’s theorem on prime PI-rings. * Supported by the Slovenian Research Agency (program No. P1-0288).

Reduced near-rings

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

Portugaliae mathematica

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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...

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)...