scholarly journals SS-Injective Modules and Rings

2017 ◽  
Vol 9 (2) ◽  
pp. 57-70
Author(s):  
Akeel Ramadan Mehdi ◽  
Adel Salim Tayyah
Keyword(s):  
Injective Modules ◽  
Small Submodule

     We introduce and investigate SS-injectivity as a generalization of both soc-injectivity and small injectivity. A right module  over a ring  is said to be SS- -injective (where  is a right -module) if every -homomorphism from a semisimple small submodule of  into  extends to . A module  is said to be SS-injective (resp. strongly SS-injective), if  is SS- -injective (resp. SS- -injective for every right -module ). Some characterizations and properties of (strongly) SS-injective modules and rings are given. Some results on soc-injectivity are extended to SS-injectivity.

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.

Psq-injective modules and rings

2021 ◽  
pp. 2250101
Author(s):  
Avanish Kumar Chaturvedi ◽  
Sandeep Kumar
Keyword(s):  
Injective Module ◽  
Injective Modules

For any two right [Formula: see text]-modules [Formula: see text] and [Formula: see text], [Formula: see text] is said to be a ps-[Formula: see text]-injective module if, any monomorphism [Formula: see text] can be extended to [Formula: see text]. Also, [Formula: see text] is called psq-injective if [Formula: see text] is a ps-[Formula: see text]-injective module. We discuss some properties and characterizations in terms of psq-injective modules.

Injective Modules, Induction Maps and Endomorphism Rings

1993 ◽  
Vol s3-67 (1) ◽  
pp. 127-158 ◽  
Author(s):  
C. J. B. Brookes ◽  
K. A. Brown
Keyword(s):  
Endomorphism Rings ◽  
Injective Modules
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