Bull. Korean Math. Soc. 2024; 61(2): 291-299
Online first article March 12, 2024 Printed March 31, 2024
https://doi.org/10.4134/BKMS.b220367
Copyright © The Korean Mathematical Society.
Sina Eftekhari, Sayyed Heidar Jafari, Mahdi Reza Khorsandi
P.O. Box 36199-95161; P.O. Box 36199-95161; P.O. Box 36199-95161
We study some factorization properties of the idealization $R$(+)$M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R$(+)$M$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $R$(+)$M$ is a BFR. We also characterize the idealization rings which are UFRs.
Keywords: Factorization, idealization, ACCP, BFR, UFR
MSC numbers: 13F15, 13B99
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