A QTAG-module is an -module, where is a limit ordinal, if is totally projective for every ordinal . In the present paper -modules are studied with the help of -pure submodules, -basic submodules, and -large submodules. It is found that an -closed -module is an -injective. For any ordinal we prove that an -large submodule of an -module is summable if and only if is summable.
Let X be a complex smooth projective variety, and G a locally free sheaf on X. We show that there is a one-to-one correspondence between pairs (Λ, Ξ), where Λ is a sheaf of almost polynomial filtered algebras over X satisfying Simpson’s axioms and is an isomorphism, and pairs (L, Σ), where L is a holomorphic Lie algebroid structure on and Σ is a class in F 1 H 2(L, ℂ), the first Hodge filtration piece of the second cohomology of L. As an application, we construct moduli spaces of semistable...
Given a hereditary torsion theory in Mod-, a module is called -supplemented if every submodule of contains a direct summand of with torsion. A submodule of is called -supplement of in if and and is -weakly supplemented if every submodule...
The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing (resp. decreasing)...