Abstract
The notion of purity is fundamental in the theory of abelian groups. Zhao introduced the concepts of nonnil relatively divisible submodules and nonnil-pure submodules. In this paper, we explore additional properties of nonnil-pure submodules by defining what we term ‘nonnil-pure exact sequences’. This new definition extends the classical concept of purity originated by P. M. Cohn. Furthermore, inspired by Fieldhouse’s work, we extend the \(\phi \)-von Neumann regular rings, previously introduced and studied by Tang, Wang, and Zhao, to modules.
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Funding
H. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2021R1I1A3047469).
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Haddaoui, Y.E., Kim, H. & Mahdou, N. On nonnil-pure theories. Beitr Algebra Geom (2024). https://doi.org/10.1007/s13366-024-00754-x
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DOI: https://doi.org/10.1007/s13366-024-00754-x
Keywords
- Nonnil-pure exact sequence
- \(\phi \)-flat module
- Nonnil-injective module
- Nonnil-FP-injective module
- \(\phi \)-von Neumann regular ring
- \(\phi \)-regular module