… In this paper, we introduce the dual concepts of presented dimensions of R-modules. We
also, introduce the copresented dimension of any R-module M: … For any R-module M, we …

… a tilting module, without the assumption that it is cotilting, we study the global dimension of its
… If P is projective non-injective we will show that in the minimal injective copresentation of P …

… module is chosen to be projective as well. More generally, in Section 4 we relate relatively
complete modules to injectively copresented modules for … with finite-dimensional modules. …

… In Section 4, we prove that there exist some equivalent characterizations of graded right
modules of n-FCP-gr-projective dimension at most k on right n-grcoherent rings. We obtain …

… copresented -comodule M to a left quasi-finitely copresented comodule Tr M. If M is
indecomposable not injective and Tr M is finite-dimensional … modules to quasi-finitely copresented …

… left modules. Then, we introduce the concept of n-weak projective right modules by using
n-super finitely copresented right modules… We also define the finitely presented dimension of R (…

… Finitely corelated modules are also called finitely copresented modules in some literatures …
if and only if every n-copresented right R-module has injective dimension at most d if and only …

… of prorational modules, which consists of inverse limits of finite-… copresentation of M to
define TrM, ie, we may omit the minimality requirement from the definition. For a finite-dimensional …

… R(M, C) = 0 for every n-copresented right R-module C of injective dimension ≤ d; a ring
R is … M is finitely cogenerated if and only if it is 0-copresented, a module M is finitely copresented …

… We say that an R-module L is n-finitely Q-copresented … The class of all n-finitely Q-copresented
modules is denoted by n-cop(Q). … → N → 0, and using the dimension shifting formula we …