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Approximations and Endomorphism Algebras of Modules
The category of all modules over a general associative ring is too complex to admit any reasonable classification. Thus, unless the ring is of finite representation type, one must limit attempts at
How To Make Ext Vanish
We describe a general construction of a module A from a given module B such that Ext(B, A) = 0, and we apply it to answer several questions on splitters, cotorsion theories and saturated rings.
Tilting Modules and Tilting Torsion Theories
Abstract We generalize basic results about classical tilting modules and partial tilting modules to the infinite dimensional case, over an arbitrary ring R. The methods employed combine classical
Tilting modules and Gorenstein rings
Abstract We apply tilting theory to study modules of finite projective dimension. We introduce the notion of finite and cofinite type for tilting and cotilting classes of modules, respectively,
Tilting theory and the finitistic dimension conjectures
Let R be a right noetherian ring and let P<∞ be the class of all finitely presented modules of finite projective dimension. We prove that findimR = n < ∞ iff there is an (infinitely generated)
'bottom'N as an abstract elementary class
Classes of generalized ∗-modules
We study the class, STAR , of all ∗-modules by means of the classes, Sλ, of all ∗λ-modules, λ> 0 being a cardinal. Since STAR, equals the intersection of the decreasing chain Sλ, λ > 0, our approach