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S. Kabbaj and
A. Mimouni
Reductions and cores of ideals in trivial ring extensions over integral domains
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| Published: |
August 5, 2026. |
| Keywords: |
Trivial ring extension, reduction, minimal reduction, core of an ideal, basic ideal, Prufer domain, valuation domain. |
| Subject [2020]: |
13A15, 13A18, 13F05, 13G05, 13F30. |
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Abstract
This paper deals with reductions and core of ideals in commutative rings. We examine trivial ring extensions arising from integral domains, particularly valuation and Prufer domains. This study builds on previous findings related to Prufer domains and earlier work on trivial ring extensions of special modules.
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| Acknowledgements
N/A
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| Author information
S. Kabbaj
Department of Mathematics
KFUPM
Dhahran 31261, KSA
kabbaj@kfupm.edu.sa
A. Mimouni
Department of Mathematics
KFUPM
Dhahran 31261, KSA
amimouni@kfupm.edu.sa
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