⋂-large pseudo injective acts
Shaymaa Amer Abdul-Kareem, Ahmed A. Abdulkareem · Journal of Discrete Mathematical Sciences and Cryptography · 2020
The purpose of introducing and studying the notion of ⋂-large pseudo-injective acts is to create a basis that facilitates the exchange of ideas between the theory of module and act theory. Furthermore, it represents a generalization of the pseudo-injective act which was presented by the author and Yan T. and can take it as a basis for future work for the researchers who work in acts theory. Besides, the concept of quasi injective S-acts over monoids was generalized to pseudo injective by the author and obtained new properties and characterization for this notion. In this paper, we continue to find another weak form of generalization for pseudo injective which is called ⋂-large pseudo injective act. Let MS and NS be two S-acts. MS is called ⋂-large pseudo-N-injective if for any ⋂-large subact X of NS, any monomorphism f from X into MS can be extended to some g from NS into MS. MS is called ⋂-large pseudo-injective if MS is ⋂-large pseudo M-injective. Major properties of mutually ⋂-large pseudo-injective acts and ⋂-large pseudo-injective acts are proved and their connections with pseudo-injective acts are addressed. Also, we have investigated the interrelationships of ⋂-reversible acts with pseudo injective acts. The conditions under which subacts of ⋂-large pseudo injective S-acts inherit the property of ⋂-large pseudo-injective have been studied.