(untitled) (Journal of the College of Basic Education, 2025)
This work aims to present novel concept that generalizes strongly extending acts previously offered through author. More precisely, concept for strongly pseudo-extending acts was introduced. substantially pseudo-extending S-act has been one at which each sub-act for has been ⋂-large at pseudo stable retract for . For any strongly pseudo-extending right (left) act S, there exists monoid S that has been strongly pseudo-extending right (left) act. each sub-acts at this act have been ⋂-large at pseudo stable retract for S-act , as well as we investigate their characterizations. This concept has been shown using examples. idea for significantly pseudo-extending acts was defined at relation to other types for injectivity. Taking things further, conditions under which sub-acts inherit property for strongly pseudo-extending acts have been investigated. concept for RP-act has been introduced. According to this concept, we obtained that strongly pseudo-extending acts have been equivalent to extending acts. Also, we illustrated at theorem (2.16) that direct sum for strongly pseudo-extending acts becomes again strongly pseudo-extending under certain conditions. 2020 Mathematics Subject Classification: 20M30, 20M99, 08B30.