However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

Infinitely generated complements to partial tilting modules Page 1 Math. Proc. Camb. Phil.
Soc. (2002), 132, 89 c© Cambridge Philosophical Society DOI: 10.1017/S0305004101005394 …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

Let M be a partial tilting module with proj. dim, 1M= t and let X be an A-module such that M
EB X is a tilting module and add M n add X= O. Then X will be called a complement to M. It is …

Finally, let B and 8 be two rings, let 9 be a full subcategory of left R-modules closed under
direct sums and factor modules, let be a full subcategory of left S-modules containing ss and …

Let TR be a 1-tilting module with tilting torsion pair (Gen T, F) in Mod-R. The following
conditions are proved to be equivalent:(1) T is pure projective;(2) Gen T is a definable …

Let M be a module over an associative ring R and σ [M] the category of M-subgenerated
modules. Generalizing the notion of a projective generator in σ [M], a module P∈ σ [M] is …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …

ALL TILTING MODULES ARE OF FINITE TYPE 1. Introduction In the early eighties Brenner
and Butler in [9] and Happel and Ringel in Page 1 PROCEEDINGS OF THE AMERICAN …

Given small dg categories A and B and a BA-bimodule T, we give necessary and sufficient
conditions for the associated derived functors of Hom and the tensor product to be fully …