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- W2952809236 abstract "It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)cap Dneq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of $R$, or $R$ has zero characteristic and there exists a natural number $n>1$ such that $frac{1}{n}in R$, then $R$ has a maximal subring. It is shown that if $R$ is a reduced ring with $|R|>2^{2^{aleph_0}}$ or $J(R)neq 0$, then any $R$-algebra has a maximal subring. Residually finite rings without maximal subrings are fully characterized. It is observed that every uncountable $UFD$ has a maximal subring. The existence of maximal subrings in a noetherian integral domain $R$, in relation to either the cardinality of the set of divisors of some of its elements or the height of its maximal ideals, is also investigated." @default.
- W2952809236 created "2019-06-27" @default.
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- W2952809236 date "2012-08-27" @default.
- W2952809236 modified "2023-09-27" @default.
- W2952809236 title "Submaximal Integral Domains" @default.
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- W2952809236 doi "https://doi.org/10.48550/arxiv.1208.5298" @default.
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