Displaying similar documents to “Stability of algebraic inverse systems, I: Stability, weak stability and the weakly-stable socle”

On a generalization of Q I -rings

Josef Jirásko (1999)

Commentationes Mathematicae Universitatis Carolinae

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In this paper rings for which every s -torsion quasi-injective module is weakly s -divisible for a hereditary preradical s are characterized in terms of the properties of the corresponding lattice of the (hereditary) preradicals. In case of a stable torsion theory these rings coincide with T Q I -rings investigated by J. Ahsan and E. Enochs in [1]. Our aim was to generalize some results concerning Q I -rings obtained by J.S. Golan and S.R. L’opez-Permouth in [12]. A characterization of the Q I -property...

Isbell duality for modules.

Barr, Michael, Kennison, John F., Raphael, R. (2009)

Theory and Applications of Categories [electronic only]

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A functorial approach to the behaviour of multidimensional control systems

Jean-François Pommaret, Alban Quadrat (2003)

International Journal of Applied Mathematics and Computer Science

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We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.

On torsionfree classes which are not precover classes

Ladislav Bican (2008)

Czechoslovak Mathematical Journal

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In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory...