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## NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS

#### Tariq Shah [1] , Waheed Ahmad Khan [2]

##### 171 184

In this article, we discuss the n-root closedness, root closedness, seminormality, S-root closedness, S-closedness, F-closedess of PVDs. A valuation domain, being integrally closed, is obviously root closed. So our interest of study is for a class of non-valuation PVDs. Let R ⊂ B be a domain extension such that R is a PVD and the common ideal P of R and B is a prime ideal in R. If R is n-root closed (respectively root closed, seminormal, S-root closed, S-closed, F-closed) in B, then R/P is PVD, which is n-root closed (respectively root closed, seminormal, S-root closed, S-closed, F-closed) in B/P. Further we study the relationship of atomic PVDs to atomic PVDs, SHFDs, LHFDs and BVDs. We also discuss a relative ascent and descent in general and particularly for the antimatter property of PVDs.
PVD, atomic domain, F + M construction, root-closed, factor ring, condition ∗, antimatter domain
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• Department of Mathematics Quaid-I-Azam University Islamabad, Pakistan e-mail: stshah@gmail.com Waheed Ahmad Khan Department of Mathematics and Statistics Caledonian College of Engineering P O Box 2322, Seeb 111, Sultanate of Oman e-mail: sirwak2003@yahoo.com
Konular JA38BY53SZ Makaleler Yazar: Tariq Shah Yazar: Waheed Ahmad Khan
 Bibtex ```@ { ieja266226, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2014}, volume = {16}, pages = {53 - 65}, doi = {10.24330/ieja.266226}, title = {NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS}, key = {cite}, author = {Khan, Waheed Ahmad and Shah, Tariq} }``` APA Shah, T , Khan, W . (2014). NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS. International Electronic Journal of Algebra, 16 (16), 53-65. DOI: 10.24330/ieja.266226 MLA Shah, T , Khan, W . "NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS". International Electronic Journal of Algebra 16 (2014): 53-65 Chicago Shah, T , Khan, W . "NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS". International Electronic Journal of Algebra 16 (2014): 53-65 RIS TY - JOUR T1 - NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS AU - Tariq Shah , Waheed Ahmad Khan Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266226 DO - 10.24330/ieja.266226 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 53 EP - 65 VL - 16 IS - 16 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266226 UR - http://dx.doi.org/10.24330/ieja.266226 Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS %A Tariq Shah , Waheed Ahmad Khan %T NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 16 %N 16 %R doi: 10.24330/ieja.266226 %U 10.24330/ieja.266226 ISNAD Shah, Tariq , Khan, Waheed Ahmad . "NOTE ON PSEUDO-VALUATION DOMAINS WHICH ARE NOT VALUATION DOMAINS". International Electronic Journal of Algebra 16 / 16 (Aralık 2014): 53-65. http://dx.doi.org/10.24330/ieja.266226