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2012•Asian-European Journal of MathematicsRequires access

MODULES SATISFYING EXTENSION CONDITIONS UNDER MONOMORPHISM OF THEIR CLOSED SUBMODULES

Truong Cong Quynh, Phan Hồng Tín

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Abstract

A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is called pseudo injective if M is pseudo M-injective. Some characterizations of classes modules and its applications to classical rings are studied. In this paper, we consider some generalizations pseudo injective modules under monomorphism of their closed submodules. Their properties are studied.

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What this paper is about

A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is called pseudo injective if M is pseudo M-injective. Some characterizations of classes modules and its applications to classical rings are studied. In this paper, we consider some generalizations pseudo injective modules under monomorphism of their closed submodules. Their properties are studied.

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Available abstract

A right R-module N is called pseudo M-injective if for any submodule A of M, every monomorphism from A to N, can be extended to a homomorphism from M to N. Module M is called pseudo injective if M is pseudo M-injective. Some characterizations of classes modules and its applications to classical rings are studied. In this paper, we consider some generalizations pseudo injective modules under monomorphism of their closed submodules. Their properties are studied.

Key concepts: Monomorphism, Injective function, Homomorphism, Mathematics, Extension (predicate logic), Injective module, Pure mathematics, Flat module

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MODULES SATISFYING EXTENSION CONDITIONS UNDER MONOMORPHISM OF THEIR CLOSED SUBMODULES — Research Paper | ScholarLens