Displaying similar documents to “[On the conference on rings and modules]”

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.

Modules with semiregular endomorphism rings

Kunio Yamagata (2008)

Colloquium Mathematicae

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We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.

Categorifications of the polynomial ring

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.

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...