Yıl 2014, Cilt 15, Sayı 15, Sayfalar 157 - 172 2014-06-01
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## ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS

#### David E. Dobbs [1]

##### 198 252

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 JA32UJ88FF Makaleler 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}, 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 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 - 2019 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