Some Results about Acts over Monoid and Bounded Linear Operators
DOI:
https://doi.org/10.21123/bsj.2024.9116Keywords:
Associated act V over monoid of sinshT, Bounded linear operator, Faithful act over monoid, One-to-one operator, Separated acts over monoidAbstract
This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that functions as an act over S if and only if functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following, is acting over S if and only if is a module where T is a nilpotent operator, is a faithful act over S, where T is any bounded linear operator, if T is any bounded operator, then is separated, if is separated act over S, Then T is injective, if a basis K = {vj, j} for V, then every element w of can be composed as =(pn (T) + . v, for some v in V, and put T as similar to any operator from to and V as a finite dimensional normed space, then is Noetherian act over S if S is Noetherian.
Received 23/05/2023
Revised 10/09/2023
Accepted 12/09/2023
Published Online First 20/02/2024
References
Abdul-Kareem SA. On Hollow acts. IOP Conf. Ser.: Mater. Sci. Eng. 2020; 928(042004): 1-14. https://doi.org/10.1088/1757-899X/928/4/042004
Ashtiania B. T., Rasoulia H., Tehraniana A., Barzegarb H., On lifting acts over monoids, Journal of Linear and Topological Algebra 2022; 11( 04), 265- 269. https://doi.org/10.30495/JLTA.2023.699063
Ashtiani B. T., Rasouli H., Tehranian A., and Barzegar H., On the notion of supplement in acts over monoids, 2023; 22(03), 2350066, https://doi.org/10.1142/S0219498823500664.
Mohammed RI, Ahmed FA. Exponential Function of a bounded Linear Operator on a Hilbert Space. Baghdad Sci. J. 2014;11(3): 1267-1273. https://doi.org/10.21123/bsj.11.3.1267-1273
Kadhim SN, Abed Z. The Act of Linear Operators. Baghdad Sci. J. 2016; 13(2): 388-393. DOI: http://dx.doi.org/10.21123/bsj.2016.13.2.0388
Kadhim SN, Ali MJM, Atiya ZA. A Note On S-acts And Bounded Linear Operators. Ital J Pure Appl Math. 2018; 39: 16–22.
Abdul-Kareem SA. Generalization of injective S-acts. Common Algebra. 2023; 51(4): 1743-1751. DOI: https://doi.org/10.1080/00927872.2022.2141766
Abdul-Kareem SA, Minimal Quasi Injective S-Acts, Int J Math Comput Sci. 2020; 15(2), 515–524ز
Abdul-Kareemi A. S., Salih S. R., Fuzzy Injective S-act On Monoids, TWMS J App Eng Math. 2021; 11(4): 1072-1079.
Al-Saadi S.A., On Locally Injective Acts over Monoids, J Southwest Jiaotong Univ, 2019; 54(6): 1-10. https://doi.org/10.35741/issn.0258-2724.54.6.54
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