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- W1608008727 abstract "The main theorem says that any module-finite (but not necessarily commutative) algebra $Lambda$ over a commutative Noetherian universally catenary ring $R$ is catenary. Hence the ring $Lambda$ is catenary if $R$ is Cohen-Macaulay. When $R$ is local and $Lambda$ is a Cohen-Macaulay $R$-module, we have that $Lambda$ is a catenary ring, $dim Lambda =dim Lambda /Q+mathrm {ht}_Lambda Q$ for any $Qin operatorname {Spec}Lambda$, and the equality $n=mathrm {ht}_Lambda Q- mathrm {ht}_Lambda P$ holds true for any pair $Psubseteq Q$ of prime ideals in $Lambda$ and for any saturated chain $P=P_0subset P_1subset cdots subset P_n=Q$ of prime ideals between $P$ and $Q$." @default.
- W1608008727 created "2016-06-24" @default.
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- W1608008727 date "1999-05-13" @default.
- W1608008727 modified "2023-10-18" @default.
- W1608008727 title "Catenarity in module-finite algebras" @default.
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- W1608008727 doi "https://doi.org/10.1090/s0002-9939-99-04962-x" @default.
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