we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

A p-indigent module is one that subprojective only to projective modules. An RD-projective any torsionfree (and flat) module. $T$ called rdp-indigent if it In this work, we consider the structure of SRDP rings whose (simple) right $R$-modules are or torsionfree. Moreover, new characterizations P-coherent and presented by subprojectivity domains.

Objective(s) The aim of this study was to investigate the overall effect of cardiac vasoactive factors during coronary occlusion and reperfusion on peripheral vascular tone, using a sequential isolated rabbit heart-ear perfusion model. Materials and Methods Isolated ears were perfused with the effluent of isolated hearts subjected to ischemia (30 min) and reperfusion (180 min, n=6). The comp...

In this paper, we introduce the notion of “(n, d)-perfect rings” which is in some way a generalization of the notion of “S-rings”. After we give some basic results of this rings and we survey the relationship between “A(n) property” and “(n, d)-perfect property”. Finally, we investigate the “(n, d)-perfect property” in pullback rings.

In this paper we introduce the notion of “strong n-perfect rings” which is in some way a generalization of the notion of “n-perfect rings”. We are mainly concerned with those class of rings in the context of pullbacks. Also we exhibit a class of n-perfect rings that are not strong n-perfect rings. Finally, we establish the transfer of this notion to the direct product notions.

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the flat-cotorsion —and prove that it, unlike dimension, behaves as one expects homological without extra assumptions on ring. Crucially, we show it coincides with where latter is finite, and right coherent rings—the setting known to behave expected.