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ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS

Year 2014, , 157 - 172, 01.06.2014
https://doi.org/10.24330/ieja.266245

Abstract

The following result uses and generalizes a recent result of Ayache
on integrally closed domains. Let R be a commutative integral domain with
integral closure R0(inside the quotient field K of R) such that each overring of
R (inside K) is a treed domain and there exists a finite maximal chain of rings
going from R to R0. Then R is a seminormal domain if and only if, for each
maximal ideal M of R, either RM is a pseudo-valuation domain or, for some
positive integer n, there exists a finite maximal chain, of length n, of rings
from RM to (RM)0 each step of which is (an integral minimal ring extension
which is) either decomposed or inert. Examples are given in which the latter
option holds where R is one-dimensional and Noetherian.

Year 2014, , 157 - 172, 01.06.2014
https://doi.org/10.24330/ieja.266245

Abstract

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Details

Other ID JA32UJ88FF
Journal Section Articles
Authors

David E. Dobbs This is me

Publication Date June 1, 2014
Published in Issue Year 2014

Cite

APA Dobbs, D. E. (2014). ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. International Electronic Journal of Algebra, 15(15), 157-172. https://doi.org/10.24330/ieja.266245
AMA Dobbs DE. ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. IEJA. June 2014;15(15):157-172. doi:10.24330/ieja.266245
Chicago Dobbs, David E. “ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS”. International Electronic Journal of Algebra 15, no. 15 (June 2014): 157-72. https://doi.org/10.24330/ieja.266245.
EndNote Dobbs DE (June 1, 2014) ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. International Electronic Journal of Algebra 15 15 157–172.
IEEE D. E. Dobbs, “ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS”, IEJA, vol. 15, no. 15, pp. 157–172, 2014, doi: 10.24330/ieja.266245.
ISNAD Dobbs, David E. “ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS”. International Electronic Journal of Algebra 15/15 (June 2014), 157-172. https://doi.org/10.24330/ieja.266245.
JAMA Dobbs DE. ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. IEJA. 2014;15:157–172.
MLA Dobbs, David E. “ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS”. International Electronic Journal of Algebra, vol. 15, no. 15, 2014, pp. 157-72, doi:10.24330/ieja.266245.
Vancouver Dobbs DE. ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. IEJA. 2014;15(15):157-72.