2025, Vol. 6, Issue 2, Part A
The connection between module theory and act theory concerns generalizations of extending act over monoids
Author(s): Shaymaa Amer Abdul-Kareem
Abstract: Generalizations of injective acts have long been a source of interest. However, no specific research has been conducted on generalizations of extending acts. This is what prompted us to propose a new generalization of extending acts, the prime-extending act. This is a generalization of the author's previous work, as well as that of J. Ahsan and Liu Zhongkui. Furthermore, because the theory of acts is a generalization of module theory, this study not only generalized the theory of acts but also Tamadher A. Ibrahiem's work in module theory. Around the same time, the idea of R-prime acts was established. Several aspects and features related to these concepts were discussed. Some results about extending acts are applied to prime-extending acts. Furthermore, certain novel features of prime-extending and R-prime acts are discussed and achieved. An S-act A is prime-extending if all non-zero proper sub-acts of A are ⋂-large in the prime retract. Furthermore, the concept of R-prime is introduced, with an S-act being considered R-prime if each proper retract is prime. It was clarified that prime-extending acts and extending acts will be the same under the R-prime act condition. Finally, it was determined that a semi-simple act and prime-extending acts are equivalent if and only if the S-act is R-prime.
DOI: https://doi.org/10.22271/math.2025.v6.i2a.223
Pages: 61-65 | Views: 588 | Downloads: 200
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How to cite this article:
Shaymaa Amer Abdul-Kareem. The connection between module theory and act theory concerns generalizations of extending act over monoids. Journal of Mathematical Problems, Equations and Statistics. 2025; 6(2): 61-65. DOI: 10.22271/math.2025.v6.i2a.223
