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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Distributive factor lattices in free rings


Author: P. M. Cohn
Journal: Proc. Amer. Math. Soc. 105 (1989), 34-41
MSC: Primary 16A06
MathSciNet review: 973837
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Abstract: For any field $ E$ with subfield $ k$ the free $ E$-ring over $ k$ on a set $ X,\quad R = {\text{ }}{E_k}\left\langle X \right\rangle $ is a fir. It is proved here that when $ E/k$ is purely inseparable, then the submodule lattice $ R/cR$ is distributive, for any $ c \ne 0$ ( $ R$ has distributive factor lattice); by contrast this is false when $ E/k$ is a nontrivial Galois extension and $ X \ne \emptyset $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0973837-3
PII: S 0002-9939(1989)0973837-3
Article copyright: © Copyright 1989 American Mathematical Society