Some Results about Acts over Monoid and Bounded Linear Operators
| Autor: | Nadia M. J. Ibrahem, Uhood S. AL-Hussani, Muna Jasim Mohammed Ali |
|---|---|
| Jazyk: | Arabic<br />English |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Baghdad Science Journal, Vol 21, Iss 9 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2078-8665 2411-7986 |
| DOI: | 10.21123/bsj.2024.9116 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|