On the generalized principally injective modules

Fatemeh Gholami; Zohreh Habibi; Alireza Najafizadeh

doi:10.4134/BKMS.b220786

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(2): 301-315

Online first article March 12, 2024 Printed March 31, 2024

https://doi.org/10.4134/BKMS.b220786

On the generalized principally injective modules

Fatemeh Gholami, Zohreh Habibi, Alireza Najafizadeh

Payame Noor University; Payame Noor University; Payame Noor University

Abstract

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Abstract

Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.

Keywords: Principally, injective, quasi

MSC numbers: Primary 13C99

Supported by: This work was financially supported by a grant from Payame Noor University of I. R. of Iran.