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## ON n-SEMIHEREDITARY AND n-COHERENT RINGS

#### Xiaoxiang Zhang [1] , Jianlong Chen [2]

##### 79 112

Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n-generated left (and/or right) ideal is flat. Some properties of n-semihereditary rings, respectively, weakly n-semihereditary rings and n-coherent rings are investigated. It is also proved that R is left n-semihereditary if and only if it is left n-coherent and weakly n-semihereditary, if and only if the ring of n × n matrices over R is left 1- semihereditary if and only if the class of all n-flat right R-modules form the torsion-free class of a torsion theory. Some known results are extended or obtained as corollaries
(weakly) n-semihereditary ring, n-coherent ring
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• Xiaoxiang Zhang and Jianlong Chen
• Department of Mathematics, Southeast University
• Nanjing 210096, P. R. China
• e-mail: z990303@seu.edu.cn (X. Zhang), jlchen@seu.edu.cn (J. Chen)
Konular JA66CV45JH Makaleler Yazar: Xiaoxiang Zhang Yazar: Jianlong Chen
 Bibtex @ { ieja266407, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2007}, volume = {1}, pages = {1 - 10}, doi = {}, title = {ON n-SEMIHEREDITARY AND n-COHERENT RINGS}, key = {cite}, author = {Zhang, Xiaoxiang and Chen, Jianlong} } APA Zhang, X , Chen, J . (2007). ON n-SEMIHEREDITARY AND n-COHERENT RINGS. International Electronic Journal of Algebra, 1 (1), 1-10. Retrieved from http://dergipark.gov.tr/ieja/issue/25210/266407 MLA Zhang, X , Chen, J . "ON n-SEMIHEREDITARY AND n-COHERENT RINGS". International Electronic Journal of Algebra 1 (2007): 1-10 Chicago Zhang, X , Chen, J . "ON n-SEMIHEREDITARY AND n-COHERENT RINGS". International Electronic Journal of Algebra 1 (2007): 1-10 RIS TY - JOUR T1 - ON n-SEMIHEREDITARY AND n-COHERENT RINGS AU - Xiaoxiang Zhang , Jianlong Chen Y1 - 2007 PY - 2007 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 1 EP - 10 VL - 1 IS - 1 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra ON n-SEMIHEREDITARY AND n-COHERENT RINGS %A Xiaoxiang Zhang , Jianlong Chen %T ON n-SEMIHEREDITARY AND n-COHERENT RINGS %D 2007 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 1 %N 1 %R %U ISNAD Zhang, Xiaoxiang , Chen, Jianlong . "ON n-SEMIHEREDITARY AND n-COHERENT RINGS". International Electronic Journal of Algebra 1 / 1 (Haziran 2007): 1-10.