scholarly journals New characterization of $\Sigma $-injective modules

2008 ◽  
Vol 136 (10) ◽  
pp. 3461-3466 ◽  
Author(s):  
K. I. Beidar ◽  
S. K. Jain ◽  
Ashish K. Srivastava
Keyword(s):  
Injective Modules

Quasi-pseudo Principally Injective Modules

2009 ◽  
Vol 16 (03) ◽  
pp. 397-402 ◽  
Author(s):  
Avanish Kumar Chaturvedi ◽  
B. M. Pandeya ◽  
A. J. Gupta
Keyword(s):  
Injective Module ◽  
Injective Modules

In this paper, the concept of quasi-pseudo principally injective modules is introduced and a characterization of commutative semi-simple rings is given in terms of quasi-pseudo principally injective modules. An example of pseudo M-p-injective module which is not M-pseudo injective is given.

scholarly journals Acyclic Complexes and Gorenstein Rings

2020 ◽  
Vol 27 (03) ◽  
pp. 575-586
Author(s):  
Sergio Estrada ◽  
Alina Iacob ◽  
Holly Zolt
Keyword(s):  
Analogous Result ◽  
Gorenstein Ring ◽  
Gorenstein Rings ◽  
Injective Modules ◽  
Flat Modules ◽  
Coherent Ring ◽  
Acyclic Complexes ◽  
Gorenstein Flat ◽  
Gorenstein Injective

For a given class of modules [Formula: see text], let [Formula: see text] be the class of exact complexes having all cycles in [Formula: see text], and dw([Formula: see text]) the class of complexes with all components in [Formula: see text]. Denote by [Formula: see text][Formula: see text] the class of Gorenstein injective R-modules. We prove that the following are equivalent over any ring R: every exact complex of injective modules is totally acyclic; every exact complex of Gorenstein injective modules is in [Formula: see text]; every complex in dw([Formula: see text][Formula: see text]) is dg-Gorenstein injective. The analogous result for complexes of flat and Gorenstein flat modules also holds over arbitrary rings. If the ring is n-perfect for some integer n ≥ 0, the three equivalent statements for flat and Gorenstein flat modules are equivalent with their counterparts for projective and projectively coresolved Gorenstein flat modules. We also prove the following characterization of Gorenstein rings. Let R be a commutative coherent ring; then the following are equivalent: (1) every exact complex of FP-injective modules has all its cycles Ding injective modules; (2) every exact complex of flat modules is F-totally acyclic, and every R-module M such that M+ is Gorenstein flat is Ding injective; (3) every exact complex of injectives has all its cycles Ding injective modules and every R-module M such that M+ is Gorenstein flat is Ding injective. If R has finite Krull dimension, statements (1)–(3) are equivalent to (4) R is a Gorenstein ring (in the sense of Iwanaga).

ESSENTIALLY SLIGHTLY COMPRESSIBLE MODULES AND RINGS

2012 ◽  
Vol 05 (02) ◽  
pp. 1250028 ◽  
Author(s):  
Abhay K. Singh
Keyword(s):  
Noetherian Ring ◽  
Slightly Compressible ◽  
Injective Modules ◽  
Nonzero Homomorphism

In this paper, the concepts of essentially slightly compressible modules and essentially slightly compressible rings are introduced, and related properties are investigated. The notion of essentially slightly compressible modules and rings are generalization of essentially compressible modules and rings introduced by [P. F. Smith and M. R. Vedadi, Essentially compressible modules and rings, J. Algebra304 (2006) 812–831]. I have also provided the characterization of such modules in terms of nonsingular injective modules. It has been shown that over a noetherian ring for a uniform module, essentially slightly compressible modules, slightly compressible modules and nonzero homomorphism from M into U for a nonzero uniform submodule U of M are equivalent. Throughout this paper, all rings are associative and all modules are unital right R-modules.

ON M-C-INJECTIVE AND SELF-C-INJECTIVE MODULES

2010 ◽  
Vol 03 (03) ◽  
pp. 387-393 ◽  
Author(s):  
A. K. Chaturvedi ◽  
B. M. Pandeya ◽  
A. M. Tripathi ◽  
O. P. Mishra
Keyword(s):  
Endomorphism Ring ◽  
Projective Module ◽  
Injective Module ◽  
Injective Modules ◽  
Factor Module ◽  
Closed Submodule

Let M1 and M2 be two R-modules. Then M2 is called M1-c-injective if every homomorphism α from K to M2, where K is a closed submodule of M1, can be extended to a homomorphism β from M1 to M2. An R-module M is called self-c-injective if M is M-c-injective. For a projective module M, it has been proved that the factor module of an M -c-injective module is M -c-injective if and only if every closed submodule of M is projective. A characterization of self-c-injective modules in terms endomorphism ring of an R-module satisfying the CM-property is given.

scholarly journals Pure Baer injective modules

1997 ◽  
Vol 20 (3) ◽  
pp. 529-538 ◽  
Author(s):  
Nada M. Al Thani
Keyword(s):  
Essential Extension ◽  
Injective Module ◽  
Algebraic Structures ◽  
Basic Properties ◽  
Injective Modules ◽  
Relative Complement

In this paper we generalize the notion of pure injectivity of modules by introducing what we call a pure Baer injective module. Some properties and some characterization of such modules are established. We also introduce two notions closely related to pure Baer injectivity; namely, the notions of a∑-pure Baer injective module and that of SSBI-ring. A ringRis an SSBI-ring if and only if every smisimpleR-module is pure Baer injective. To investigate such algebraic structures we had to define what we callp-essential extension modules, pure relative complement submodules, left pure hereditary rings and some other related notions. The basic properties of these concepts and their interrelationships are explored, and are further related to the notions of pure split modules.

Characterization of rings using finite-direct-injective modules

2019 ◽  
Vol 13 (07) ◽  
pp. 2050133
Author(s):  
Sanjeev Kumar Maurya ◽  
A. J. Gupta
Keyword(s):  
Injective Module ◽  
Artinian Rings ◽  
Injective Modules

In this paper, we characterize strongly right [Formula: see text]-rings in terms of finite-direct-injective modules which is a generalization of direct-injective modules (or [Formula: see text]-modules). Using this result, we give an example of a finite-direct-injective module which is not a direct-injective module. We prove that if every finite-direct-injective right [Formula: see text]-module is a direct-injective module, then the ring [Formula: see text] must be right Noetherian. Also, we characterize semisimple artinian rings, regular right FGC-rings in terms of finite-direct-injective modules.

scholarly journals KARAKTERISASI MODUL CYCLICALLY PURE (CP)-INJEKTIF

2020 ◽  
Vol 3 (1) ◽  
pp. 1-14
Author(s):  
Nia Yulianti ◽  
Hanni Garminia Y
Keyword(s):  
Commutative Ring ◽  
Injective Module ◽  
Injective Modules ◽  
Pure Extension

This research deals with the structure of cyclically pure injective modules over a commutative ring R. If I be an ideal of R, proved that any CP-injective R/Imodul is also CP-injective as an R-module. The main result of research is the existance of CP-injective R-module if there is an R-module. More over, we deal characterization of CP-injective module which is related to proper essential ctclically pure extension. It is shown that R-modul D is cyclically pure injective if and only if D has no proper essential cyclically pure extension.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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