On subinjectivity domains of RD-injective modules

2021 ◽  
Author(s):  
Yılmaz Durğun
Keyword(s):  
Injective Modules ◽  
Divisible Modules

The subjectivity domain of a module allows us to evaluate how close (or far) a module is from being injective. In this paper, we consider three families of rings characterized by their RD-injective left [Formula: see text]-modules via the subinjective domain: those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to divisible modules, those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to fp-injective modules and those whose noninjective RD-injective left [Formula: see text]-modules are subinjective relatively only to injective modules.

Injective modules and divisible modules over hereditary rings

2015 ◽  
Vol 7 (4) ◽  
pp. 299-308
Author(s):  
Alberto Facchini ◽  
Mai Hoang Bien
Keyword(s):  
Injective Modules ◽  
Divisible Modules

On the flat length of injective modules

2011 ◽  
Vol 84 (2) ◽  
pp. 408-432 ◽  
Author(s):  
Ioannis Emmanouil ◽  
Olympia Talelli
Keyword(s):  
Injective Modules

On GI-Injective Modules

2012 ◽  
Vol 40 (10) ◽  
pp. 3841-3858 ◽  
Author(s):  
Zenghui Gao
Keyword(s):  
Injective Modules

scholarly journals Injective modules under faithfully flat ring extensions

2015 ◽  
Vol 144 (3) ◽  
pp. 1015-1020 ◽  
Author(s):  
Lars Winther Christensen ◽  
Fatih Köksal
Keyword(s):  
Injective Modules ◽  
Flat Ring ◽  
Ring Extensions

Ramification Indices and Injective Modules

1975 ◽  
Vol s2-11 (3) ◽  
pp. 267-275 ◽  
Author(s):  
Rodney Y. Sharp
Keyword(s):  
Injective Modules

Four concepts from “geometrical” stability theory in modules

1992 ◽  
Vol 57 (2) ◽  
pp. 724-740 ◽  
Author(s):  
T. G. Kucera ◽  
M. Prest
Keyword(s):  
Model Theory ◽  
Stability Theory ◽  
The Other ◽  
General Stability ◽  
Injective Modules ◽  
Algebraic Problem

In [H1] Hrushovski introduced a number of ideas concerning the relations between types which have proved to be of importance in stability theory. These relations allow the geometries associated to various types to be connected. In this paper we consider the meaning of these concepts in modules (and more generally in abelian structures). In particular, we provide algebraic characterisations of notions such as hereditary orthogonality, “p -internal” and “p-simple”. These characterisations are in the same spirit as the algebraic characterisations of such concepts as orthogonality and regularity, that have already proved so useful. Of the concepts that we consider, p-simplicity is dealt with in [H3] and the other three concepts in [H2].The descriptions arose out of our desire to develop some intuition for these ideas. We think that our characterisations may well be useful in the same way to others, particularly since our examples are algebraically uncomplicated and so understanding them does not require expertise in the model theory of modules. Furthermore, in view of the increasing importance of these notions, the results themselves are likely to be directly useful in the model-theoretic study of modules and, via abelian structures, in more general stability-theoretic contexts. Finally, some of our characterisations suggest that these ideas may be relevant to the algebraic problem of understanding the structure of indecomposable injective modules.

Injective modules and prime ideals

1981 ◽  
Vol 9 (9) ◽  
pp. 989-999 ◽  
Author(s):  
P.F. Smith
Keyword(s):  
Prime Ideals ◽  
Injective Modules

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

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