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2023•Journal of Al-Qadisiyah for Computer Science and MathematicsOpen access

SAS-Injective Modules

Heba Hadi Chyad, Akeel Ramadan Mehdi

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Abstract

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

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

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Available abstract

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

Key concepts: Injective function, Injective module, Module, Monomorphism, Mathematics, Homomorphism, Generalization, Divisible group

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