About One of the Generalizations of Extending Acts

Abstract

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.