ON GENERALIZATION OF EXTENDING ACTS AND M-JECTIVE ACTS

MATTER: International Journal of Science and Technology

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Field Value
 
Title ON GENERALIZATION OF EXTENDING ACTS AND M-JECTIVE ACTS
 
Creator Abdul-Kareem, Shaymaa Amer
 
Subject Generalization of Extending Acts
M-JECTIVE ACTS
Direct Sums of Uniform Acts
Indecomposable Acts
Absolute Relative Jective Act (ARJ-act)
Extending Acts
 
Description An S-act  is called a generalized extending act (for short a GE-act) if the following condition is satisfied: If  =     , and X is subact of, then there exist  is a retract of  (i = 1, 2) such that     is a complement of X in . In this article, the notion of generalized extending S-act is introduced and studied as a concept of generalizing extending act which was presented by the author. Some properties of such acts in analogy with the known properties for extending acts are illustrated .Besides, the author has introduced in a diagram of acts and homomorphisms, the concept of generalized of quasi injective which is also representing a generalization of M-injective acts. Here we introduce the concept of M-jective acts, which is a generalization of the concept of M-injectivity. An S-act Y is called X-jective if every complement Z of Y in  is a retract, where  = X Y. The concept of M-jective acts is used here to solve the problem of finding a necessary and sufficient condition for a direct sum of extending acts to be extending. Indeed, we show that relative jectivity is necessary and sufficient for a direct sum of two extending acts to be extending as in module theory. Some properties and characterizations of generalizing extending act and M-jective act are illustrated. Conditions on which subact inherit the property of generalizing extending act were demonstrated. The relationship among extending act and generalizing extending act, act with condition and generalizing extending act was elucidated. Conclusions and discussion of this work were clarified in the last section. Article DOI: https://dx.doi.org/10.20319/mijst.2019.51.7384 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
 
Publisher GRDS Publishing
 
Date 2019-04-09
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Peer-reviewed Article
 
Format application/pdf
 
Identifier https://grdspublishing.org/index.php/matter/article/view/1898
 
Source MATTER: International Journal of Science and Technology; Vol 5 No 1 (2019): Regular Issue
2454-5880
 
Language eng
 
Relation https://grdspublishing.org/index.php/matter/article/view/1898/3412
 
Rights Copyright (c) 2019 Shaymaa Amer Abdul-Kareem
 

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