Pseudo injective systems

What is it about?

The notion of Pseudo Finitely Quasi-Injective systems over monoids can be viewed from both sides it is a generalization to the topic of the finitely quasi-injective system and on the other hand, it is a generalization to the topic of the pseudo injective system over monoids. This notion was studied as injectivity relative to a class of finitely generated subsystems. Several properties of this kind of generalization, as well as their characterizations, were discussed. Conditions under which subsystems of pseudo finitely quasi-injective system inherit this property. The relationship between the classes of pseudo finitely quasi-injective with other classes of injectivity was studied.

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Why is it important?

We adopt this notion of Pseudo Finitely Quasi-Injective systems over monoids because it can be viewed from both sides it is a generalization to the topic of the finitely quasi-injective system and on the other hand, it is a generalization to the topic of the pseudo injective system over monoids. Two significant findings are that: 1) In proposition (3.1), we found the relationship between this notion with the injective system and this is an important way when someone gives any generalization to some notions. 2) In theorem(2.5), we gave a characterization to this notion and this important way to know what the important thing on this subject.

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