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IMCS/Publications/BASM/Issues/BASM n.3(88), 2018/

On pseudo-injective and pseudo-projective modules

Authors: Alejandro Alvarado-García, Cèsar Cejudo-Castilla, Tania Gabriela Pérez-Quijano, Ivan Fernando Vilchis-Montalvo

Abstract

In this work we obtain characterizations of $QI$ rings and semisimple rings using quasi-injective and pseudo-injective modules respectively. We define and construct the pseudo-injective hull of a module and we give sufficient conditions on a ring to have the following properties: every pseudo-injective module is pseudo-projective and every pseudo-projective module is pseudo-injective. We also give some properties of the big lattice of classes of modules being closed under submodules and quasi-injective hulls.

Alejandro Alvarado-García
Tania Gabriela Pérez-Quijano
Facultad de Ciencias
Universidad Nacional Autónoma de México
Circuito Exterior, C.U.,C.P. 04510
Ciudad de México, México
E-mail: ,

César Cejudo-Castilla
Ivan Fernando Vilchis-Montalvo
Facultad de Ciencias Físico Matemáticas
Benemérita Universidad Aut´ onoma de Puebla
Av. San Claudio y 18 Sur, Col. San Manuel, C.U.,
C.P. 7257, Puebla, México
E-mail: ,

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