We introduce and investigate SS-injectivity as a generalization of both soc-injectivity and small injectivity. A right module  over a ring  is said to be SS- -injective (where  is a right -module) if every -homomorphism from a semisimple small submodule of  into  extends to . A module  is said to be SS-injective (resp. strongly SS-injective), if  is SS- -injective (resp. SS- -injective for every right -module ). Some characterizations and properties of (strongly) SS-injective modules and rings are given. Some results on soc-injectivity are extended to SS-injectivity.

This study presents the notion of neutrosophic Z-algebra and neutrosophic pseudo Z-algebra explores some of its properties. Also studied are the neutrosophic Z-ideal, neutrosophic Z-sub algebra, and neutrosophic Z-filter. Several properties are discovered, and some findings from the study of homomorphism are discussed.