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Volume 8, Issue 5, October 2019, Page: 88-92
About the Closed Quasi Injective S-Acts Over Monoids
Shaymaa Amer Abdul-Kareem, Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Ahmed Amer Abdulkareem, Department of Computer Science, College of Science, Mustansiriyah University, Baghdad, Iraq
Received: Sep. 8, 2019;       Accepted: Oct. 15, 2019;       Published: Oct. 24, 2019
DOI: 10.11648/j.pamj.20190805.12      View  627      Downloads  156
The aim of introducing and studying the notion of closed quasi injective S-act is to create a basis facilitate for the exchange ideas between module theory and act theory. As well as it represents a generalization of the quasi-injective act. The quasi-injective act was first introduced and studied by A. M. Lopez, Jr. and J. K. Luedeman, 1979. Then the author was one of the researchers which introduced several generalizations for this notion from several aspects because of its importance. More accurately, the contribution of this paper to the field of competence can be summarized into three points as follows: First: The possibilities for applying the topic of this article helps researchers about how can connect class of injectivity with its generalizations. Second: Study the topic of this article contributes to the improvement of the vision for finding the corresponding between acts theory and module theory. Third: This article has dealt with the important subject in the field of science and knowledge especially in algebra and can take it as a basis for future work for the researchers who work on algebra. Now, in this paper, the concept of closed quasi injective acts over monoids is introduced which represents a generalization of quasi injective. Several characterizations of this concept are given to show the behavior of the property of closed quasi injective. Relationship of the concept of closed quasi injective acts over monoids with Hopfian, co-Hopfian and directly finite property are considered. This work gives the answer to the question of what are the conditions to be met in the subacts in order to inherit the property of closed quasi injectivity. We obtained the main result in this direction in proposition (2.5) and proposition (2.6). A part of this paper was devoted to studying the relationship among the class of closed quasi injective acts with some generalizations of injectivity.
Closed Quasi Injective Acts, Extending Acts, Continuous Acts, Noetherian Acts, Hopfian Acts
To cite this article
Shaymaa Amer Abdul-Kareem, Ahmed Amer Abdulkareem, About the Closed Quasi Injective S-Acts Over Monoids, Pure and Applied Mathematics Journal. Special Issue: Algebra with Its Applications. Vol. 8, No. 5, 2019, pp. 88-92. doi: 10.11648/j.pamj.20190805.12
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
M. Kilp, U. Knauer, & A. V. Mikhalev, “Monoids acts and categories with applications to wreath products and graphs”, a handbook for students and researchers, Berlin, W. de Gruyter, (2000). Retrieved from
A. Shaymaa, “About the generalizations in systems over monoids”, LAP LAMBERT Academic Publishing, Germany, (2018). Retrieved from
A. Shaymaa, “Generalizations of quasi injective acts over monoids”, PhD. thesis, College of Science, University of Al-Mustansiriyah, Baghdad, Iraq, (2015). Retrieved from
A. Shaymaa, “Pseudo C-M-injective and pseudo C-quasi principally injective acts over monoids”, Journal of Progressive Research in Mathematics (JPRM), 6 (3), pp. 788-802, (2016). Retrieved from
A. Shaymaa, “Pseudo IC-injective systems over monoids”, Global Journal of mathematics (GJM), 6 (3), pp. 636-642, (2016). Retrieved from
Berthiaume P., “The injective envelope of S-sets”, Canad. Math. Bull., 10 (2), pp. 261–272, (1967). Retrieved from
Shaymaa A., “On Finitely Generated in S-systems over monoids”, Noor Publishing, Germany, (2018). Retrieved from
T.Yan, “Generalized injective S-acts on a monoid”, Advances in mathematics, 40 (4), pp. 421-432, (2011). Retrieved from
K. Sungjin and K. Jupil, “Weakly large subacts of S-act”, J. of Chungcheong Math. Soc., 20 (4), pp486-493, (2007).
C. V. Hinkle and Jr., “The extended centralizer of an S-set”, Pacific journal of mathematics, 53 (1), pp163-170, (1974). Retrieved from
J. Ahsan, “Monoids characterized by their quasi injective S-acts”, Semigroup forum, 36 (3), pp 285-292, (1987). Retrieved from
A. M. Lopez, Jr. and J. K. Luedeman, “Quasi-injective S-acts and their S-endomorphism Semigroup”, Czechoslovak Math. J., 29 (104), pp97-104, (1979). Retrieved from
M. S. Abbas and A. Shaymaa, “Principally quasi injective act over monoid”, Journal of advances in mathematics, 10 (1), 3152-3162, (2015). Retrieved from
A. Shaymaa, “Extending and P-extending S-act over Monoids”, International Journal of Advanced Scientific and Technical Research, 2 (7), pp. 171-178, (2017). Retrieved from
A. K. Tiwary, S. A. Paramhans, and B. M. Pandeya, “Generalization of quasi injectivity”, Progress of Mathematics, 13 (1-2), pp. 31-40, (1979).
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