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Czechoslovak Mathematical Journal, Vol. 74, No. 2, pp. 389-395, 2024

Maximal non-pseudovaluation subrings of an integral domain

Rahul Kumar

Received March 21, 2023.   Published online June 5, 2024.
Abstract:  The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain.
Keywords:  maximal non-pseudovaluation domain; pseudovaluation subring
Classification MSC:  13B02, 13G05, 3F30, 13B22
DOI:  10.21136/CMJ.2024.0122-23
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Affiliations:   Rahul Kumar, Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani 333031, Rajasthan, India, e-mail: rahulkmr977@gmail.com
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