A WEAK FORM FOR EXTENDING ACTS

Authors:

Shaymaa Amer Abdul-Kareem,

DOI NO:

https://doi.org/10.26782/jmcms.2024.08.00012

Keywords:

Semi ⋂-large sub-acts,⋂-large sub-acts,strongly closed sub-acts,Closed sub-acts,fully ⋂-large acts,

Abstract

Important areas for study in the field of act theory include expansions for the notion for extending acts. There has already been an introduction to the idea of extending acts. Our focus recently has been on semi-extending acts as a means for investigating one of these generalizations. The condition that every sub-act for an S-act  has been semi -large in a retracted from has been what defines it as a semi-extending S-act. Based on this, we provide several characteristics for semi-extending acts. Also included are examples that show how this idea works. We prove relationships between semi-extending acts and related conceptions utilizing a fully essential notion.

Refference:

I. J. Ahsan and L.Zhongkui, prime and semiprime acts over monoids with zero, Math.J., Ibaraki University, Vol.33, pp. 9 – 15, 2001. https://www.researchgate.net/publication/251080153_Prime_and_semiprime_acts_over_monoids_with_zero
II. Z. A. AL-Bast and P. F. Smith, Multiplication modules, Communication in Algebra, Vol. 10, 755-779, 2007. https://www.tandfonline.com/doi/pdf/10.1080/00927878808823601
III. P. Berthiaume, The injective envelope for S-sets, Canad . Math. Bull.,10, 261 – 273, 2018. https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/injective-envelope-of-ssets/CC5C688B45202403E48AE8B5C75CEC0F
IV. N. V. Dungh, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending modules, Pitman Researh Notes in Mathematics Series 313, Longmon, New York, 2019. https://www.researchgate.net/publication/330967788_Extending_modules
V. E. H., Feller and R. L.Gantos, Indecomposable and injective S-acts with zero , Math.Nachr., 41, pp37-48,1969. https://doi.org/10.1002/mana.19690410104
VI. C. V. Hinkle and Jr., The extended centralizer of an S-set, Pacific journal for mathematics, Vol.53, No.1, pp163-170, 1974. https://msp.org/pjm/1974/53-1/pjm-v53-n1-p14-s.pdf
VII. M. Kilp, U. Knauer and A.V. Mikhalev, Monoids acts and categories. Walter de Gruyter, Berlin, New York, 2000. https://doi.org/10.1515/9783110812909
VIII. A. M. Lopez, Jr. and J. K. Luedeman, Quasi-injective S-acts and their S-endomorphism Semigroup, Czechoslovak Math.J., Vol. 29, No.104, pp 97-104,1979. https://eudml.org/doc/13107
IX. A. M. Lopez, Jr. and J.K.Luedeman , The Bicommutator for the injective hull for a non- singular semigroup , Semigroup forum , Vol.12 , pp71-77, 1976. https://link.springer.com/article/10.1007/BF02195910
X. R. Mohammad and E.Majid, Strongly duo and duo right S-acts , Italian journal for pure and applied mathematics,32, 143-154, 2014. https://ijpam.uniud.it/online_issue/201432/14-RooeintanErshad.pdf
XI. A. Shaymaa , Generalizations of injective S-acts, Communications in algebra, Vol.51,No.4 , PP.1743-1751, 2022. https://doi.org/10.1080/00927872.2022.2141766
XII. A. Shaymaa and A. A. Ahmed, ⋂-large pseudo injective acts, Journal for discrete mathematical sciences and cryptography, Vol.25, No.2, PP.511-522, 2022. DOI:10.1080/09720529.2020.1734294
XIII. A. Shaymaa, Extending and P-extending S-act over monoids , International Journal for advanced scientific and technical research, Vol.2 , No. 7, pp.171-178,2017. https://rspublication.com/ijst/2017/april17/19.pdf
XIV. K. Sungjin and K.Jupil , Weakly large subsystems of S-system , J. for Chungcheong Math. Soc., Vol.20, no.4, pp486-493,2007. http://www.ccms.or.kr/data/pdfpaper/jcms20_4/20_4_485.pdf
XV. T. Yan , A.Javed , X.FEI and G.XIAO, Monoids characterized by their injectivity and projectivity classes, Advances in mathematics, Vol.36,No.3 ,pp. 321-326,2007. http://china.oriprobe.com/articles/12275678/Monoids_Characterized_by_Their_Injectivity_and_Pro.htm

View Download