Yıl 2014, Cilt 15, Sayı 15, Sayfalar 157 - 172 2014-06-01

ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS

David E. Dobbs [1]

190 231

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.
Minimal ring extension, FCP, integral domain, overring, treed domain, pseudo-valuation domain, seminormal, integral closure, i-domain
Konular
Diğer ID JA32UJ88FF
Dergi Bölümü Makaleler
Yazarlar

Yazar: David E. Dobbs

Bibtex @ { ieja266245, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2014}, volume = {15}, pages = {157 - 172}, doi = {10.24330/ieja.266245}, title = {ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS}, key = {cite}, author = {Dobbs, David E.} }
APA Dobbs, D . (2014). ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS. International Electronic Journal of Algebra, 15 (15), 157-172. DOI: 10.24330/ieja.266245
MLA Dobbs, D . "ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS". International Electronic Journal of Algebra 15 (2014): 157-172 <http://dergipark.gov.tr/ieja/issue/25196/266245>
Chicago Dobbs, D . "ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS". International Electronic Journal of Algebra 15 (2014): 157-172
RIS TY - JOUR T1 - ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS AU - David E. Dobbs Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266245 DO - 10.24330/ieja.266245 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 157 EP - 172 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266245 UR - http://dx.doi.org/10.24330/ieja.266245 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS %A David E. Dobbs %T ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266245 %U 10.24330/ieja.266245
ISNAD Dobbs, David E. . "ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS". International Electronic Journal of Algebra 15 / 15 (Haziran 2014): 157-172. http://dx.doi.org/10.24330/ieja.266245