Let R be a ring. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

In this paper, we show how to reformulate the fractional representation approach to analysis
and synthesis problems within an algebraic analysis framework. In terms of modules, we …

In (4), Connell proved that RG is a Noetherian ring if and only if R is a Noetherian ring and G
is a finitely generated group. Motivated by this result we ask when is RG a coherent ring …

The main result is that the ring of polynomials in any number of variables over a
commutative absolutely flat ring is coherent. The proof uses the most elementary part of G …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

The homological properties of pure modules are considered, showing, in particular, that for
coherent rings the pure modules occupy roughly the same position with respect to injective …

Let $ R $ be a commutative ring. We first derive necessary and sufficient conditions for the
rings $ R\left\langle x\right\rangle $ and $ R (x) $ to be coherent. Next, for stably coherent …

In this paper, we investigate Gorenstein FC-projective modules and Gorenstein FC-
projective dimensions, and characterize rings over which every module is Gorenstein FC …

An R-module M is called strongly FP-injective if Ext R i (P, M)= 0 for any finitely presented R-
module P and any i> 0. Denoted by SFI the class of all strongly FP-injective R-modules and …

Подмодуль AczB называется ч и с т ы м в£, если отображение М® А-* М® В
мономорфно для любого правого модуля М. Будем назы вать модуль А ч и с т ы м, если …