… even when N-products of copies of one injective module are injective (131). Now we will
discover when the N-product of copies of one flat module is flat (ie, when it is nu-flat). To answer …

… subdirect products. The main objective is to characterize the flatness and projectivity of these
subdirect products of flat and projective modules … the M-product of flat R-modules to be flat (…

… which N-products of flat graded modules are flat (Theorem 3.7… N-products of copies of one
flat graded module U are flat (… of the N-product in the categories of graded modules, that is, …

… R-modules to split in the corresponding direct product were given. In the present paper, we
… for the U-product of R-modules to split in the corresponding direct product (Theorem 4). This …

… Indeed, K-products are special cases of a larger class of submodules of the direct … We
can now generalize the classical result about direct products of flat modules (we also extend …

… (It should be remarked that a large class of rings from classical … submodules of a, flat
module can be obtained. Proposition S. Let pU be flat, and P s U, Then P is pure in U = U/P is flat. …

… subalgebras is fairly large - in particular, large enough to obtain all possible flat dimensions.
… Hence, E is semi-simple as a subdirect product of semisimple rings. b) Let I be a projective …

… subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories
and functors, flat modules… The next definition gives a large source of modules which will …

… , injective, flat, semisimple, regular, and finite-dimensional (in the sense of Goldie) modules.
… Also, in Chapter 6 we use Hattori torsion-free modules [74], [76] to study flat modules. In …

… module M R is local if M R has a largest proper submodule, that is, if M R is a cyclic module
… There is a commutative diagram in which the horizontal arrows are subdirect products of …