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A note on pinched extensions
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DOI：10.21136/CMJ.2026.0256-25.png)
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Abstract
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We say R subset of S is pinched at some intermediate ring R0, where R subset of R0 subset of S, if each intermediate ring between R and S is comparable to R0 under inclusion. A new characterization of Pr & uuml;fer extensions in terms of maximal excluding domains is given. We also characterize minimal extensions of a Pr & uuml;fer domain and prove that no extension of a one-dimensional Pr & uuml;fer domain can be pinched, and thereby extending old results of Gilbert on lambda-extensions. Next, we show that a proper finite Galois extension is pinched if and only if the Galois group is cyclic of prime power order. Further, the preservation of comparability of the integral closure and that of lambda-finiteness in pullbacks is also studied.
Keywords:
comparable overring
integral closure
Pr & uuml
fer extension
Pinched extension
pullback
support of a module
Journal
C
IF:
0.5
Papers:
60
Citations:
0