A short survey on Gorenstein global dimension
Driss Bennis (2010)
Actes des rencontres du CIRM
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This text gives a short overview of the recent works on Gorenstein global dimension of rings.
Driss Bennis (2010)
Actes des rencontres du CIRM
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This text gives a short overview of the recent works on Gorenstein global dimension of rings.
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.
Mikhail Khovanov, Radmila Sazdanovic (2015)
Fundamenta Mathematicae
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We develop a diagrammatic categorification of the polynomial ring ℤ[x]. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xⁿ and standard modules to (x-1)ⁿ in the Grothendieck ring.
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...
José L. Gómez Pardo (1989)
Extracta Mathematicae
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Pimenov, K.I. (2002)
Zapiski Nauchnykh Seminarov POMI
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Christian Gottlieb (1994)
Manuscripta mathematica
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Juan Jacobo Simón Pinero (1992)
Publicacions Matemàtiques
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In this paper we compute the global dimension of Noetherian rings and rings with Gabriel and Krull dimension by taking a subclass of cyclic modules determined by the Gabriel filtration in the lattice of hereditary torsion theories.
Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)
Colloquium Mathematicae
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Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically...
Samir Bouchiba (2013)
Colloquium Mathematicae
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We present an alternative way of measuring the Gorenstein projective (resp., injective) dimension of modules via a new type of complete projective (resp., injective) resolutions. As an application, we easily recover well known theorems such as the Auslander-Bridger formula. Our approach allows us to relate the Gorenstein global dimension of a ring R to the cohomological invariants silp(R) and spli(R) introduced by Gedrich and Gruenberg by proving that leftG-gldim(R) = maxleftsilp(R),...
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...
K.R. Goodearl, R.B. Jr. Warfield (1982)
Mathematische Zeitschrift
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K.R. Goodearl, P.C. Eklof, J. Trlifaj (1997)
Forum mathematicum
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