Displaying similar documents to “Fiber products and Morita duality for commutative rings”

Finite dimensional rings of quotients.

H. Leroy Hutson (1993)

Publicacions Matemàtiques

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In this paper we characterize commutative rings with finite dimensional classical ring of quotients. To illustrate the diversity of behavior of these rings we examine the case of local rings and FPF rings. Our results extend earlier work on rings with zero-dimensional rings of quotients.

There is no analog of the transpose map for infinite matrices.

Juan Jacobo Simón (1997)

Publicacions Matemàtiques

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In this note we show that there are no ring anti-isomorphism between row finite matrix rings. As a consequence we show that row finite and column finite matrix rings cannot be either isomorphic or Morita equivalent rings. We also show that antiisomorphisms between endomorphism rings of infinitely generated projective modules may exist.

Quasi-Frobenius quotient rings.

José Gómez Torrecillas, Blas Torrecillas Jover (1991)

Extracta Mathematicae

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Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modules permits to achieve homological characterizations for some kinds of rings (regular Von Neumann, hereditary). Colby investigated in [1] the rings with the property that every left R-module is embedded in a flat left R-module and called them left IF rings. These rings include regular and quasi-Frobenius rings. Another useful tool for the study of non-commutative rings is the classical...

The First Isomorphism Theorem and Other Properties of Rings

Artur Korniłowicz, Christoph Schwarzweller (2014)

Formalized Mathematics

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Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial

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)...

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X⊥ of a subset X of R is zero, then X1 ⊥ = 0 for a finite subset X1 ⊆ X. (ZIP 2) If L is a left ideal and if L⊥ = 0, then L1 ...