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- W2123458831 abstract "Let D be an integral domain with identity. In (3), Cohn has shown that if D is a Schreier ring, then D can be inertly embedded in a pre-Bezout domain B( D ), which Cohn calls the pre-Bezout hull of D . Further, D is an HCF-ring if and only if B( D ) is a Bezout domain, and D is a UFD if and only if B( D ) is a PID. Using a modification of Cohn's techniques, Samuel in (8) has shown that a Krull domain can be inertly embedded in a Dedekind domain. In this paper, we show that these embedding theorems are also obtained by considering the embedding of a v -ring in its Kronecker function ring with respect to the v -operation. To wit, if D is a v -ring and if D v is the Kronecker function ring of D with respect to the v -operation, then D v is a Bezout domain, and we show that D is inertly embedded in D v if an only if D is an HCF-ring. Moreover, D is a UFD if and only if D v is a PID, and if D is a Krull domain, D is inertly embedded (in Samuel's sense) in D v , a Dedekind domain." @default.
- W2123458831 created "2016-06-24" @default.
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- W2123458831 date "1970-11-01" @default.
- W2123458831 modified "2023-10-17" @default.
- W2123458831 title "An embedding theorem for HCF-rings" @default.
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- W2123458831 doi "https://doi.org/10.1017/s0305004100076568" @default.
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