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Maximal non valuation domains in an integral domain

Rahul Kumar, Atul Gaur (2020)

Czechoslovak Mathematical Journal

Let R be a commutative ring with unity. The notion of maximal non valuation domain in an integral domain is introduced and characterized. A proper subring R of an integral domain S is called a maximal non valuation domain in S if R is not a valuation subring of S , and for any ring T such that R ⊂ T ⊂ S , T is a valuation subring of S . For a local domain S , the equivalence of an integrally closed maximal non VD in S and a maximal non local subring of S is established. The relation between dim ( R , S ) and the number...

Maximal non-pseudovaluation subrings of an integral domain

Rahul Kumar (2024)

Czechoslovak Mathematical Journal

The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let R ⊂ 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 ⊂ T ⊂ 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.

On a non-vanishing Ext

Laszlo Fuchs, Saharon Shelah (2003)

Rendiconti del Seminario Matematico della Università di Padova

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