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On the Stable Radical of Some Non-Domestic String Algebras
We introduce the concept of a prime band in a string algebra Λ and use it to associate to Λ its finite bridge quiver. Then we introduce a new...
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Weakly Stable Torsion Classes
Weakly stable torsion classes were introduced by the author and Yekutieli to provide a torsion theoretic characterisation of the notion of weak...
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New results on C 11 and C 12 lattices with applications to Grothendieck categories and torsion theories
In this paper, which is a continuation of our previous paper [T. Albu, M. Iosif, A. Tercan, The conditions ( C i ) in modular lattices, and applications ...
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Dimension and decomposition in modular upper-continuous lattices
We translate notions and results of decomposition and dimension theories for module categories into the lattice environment. In particular, we...
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Galois Connections Between Lattices of Preradicals Induced by Adjoint Pairs Between Categories of Modules
We extend the result which establishes that every equivalence between categories of modules induces an isomorphism between the corresponding lattices...
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Recollements of Module Categories
We establish a correspondence between recollements of abelian categories up to equivalence and certain
TTF -triples. For a module category we show,... -
Köthe’s upper nil radical for modules
Let M be a left R -module. In this paper a generalization of the notion of an s -system of rings to modules is given. Let N be a submodule of M . Define
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Strongly Semihereditary Rings and Rings with Dimension
The existence of a well-behaved dimension of a finite von Neumann algebra (see Lück, J Reine Angew Math 495:135–162,
1998 ) has lead to the study of... -
On τ-Extending Modules
Motivated by [2] and [6], we introduce a generalization of extending (CS) modules by using the concept of τ -large submodule which was defined in [9]....
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A Note on (α, β)-higher Derivations and their Extensions to Modules of Quotients
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of (α, β)-derivation to (α,...
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A Seventy Years Jubilee: The Hopkins-Levitzki Theorem
The aim of this expository paper is to discuss various aspects of the Hopkins-Levitzki Theorem (H-LT), including the Relative H-LT, the Absolute or...
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A Theory of Hulls for Rings and Modules
In this expository paper, we survey results on the concept of a hull of a ring or a module with respect to a specific class of rings or modules. A...
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When Does the Rational Torsion Split Off for Finitely Generated Modules
It is well known that the torsion part of any finitely generated module over the formal power series ring K [[ X ]] is a direct summand. In fact, K [[ X ]]...
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On torsionfree classes which are not precover classes
In the class of all exact torsion theories the torsionfree classes are cover (pre-cover) classes if and only if the classes of torsionfree relatively...
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Extending modules relative to a torsion theory
An R -module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the...