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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 李白飛 教授(Pjek-Hwee Lee) | |
| dc.contributor.author | Shao-Chi Lee | en |
| dc.contributor.author | 李詔琦 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:58:48Z | - |
| dc.date.available | 2016-07-26 | |
| dc.date.copyright | 2016-07-26 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-07-13 | |
| dc.identifier.citation | [1] E.P. Armendariz, H.K. Koo, J.K. Park. Isomorphic Ore extensions. Comm. Algebra.15(12)(1987), 2633–2652. 20
[2] Smoktunowicz, A. Polynomial rings over nil rings need not be nil. Journal of Algebra. 233 (2003), 427–436. [3] A. M. Babic. The Levitzki radical. (Russian) Dokl. Akad. Nauk., SSSR 126 (1959). 242-243. [4] G.F. Birkenmeier, H.E. Heatherly, E.K. Lee. Completely prime ideals and associated radicals. World Sci. Publ. (1993), 102–129. [5] G.F. Birkenmeier, J.Y. Kim, J.K. Park. Regularity conditions and the simplicity of prime factor rings. J. Pure Appl. Algebra. 115 (1997), 213–230. [6] G.F. Birkenmeier, H.E. Heatherly, E.K. Lee. ”Completely prime ideals and radicals in near-rings”. Proc. Near-Rings and Near-Fields Conf. Kluwer, (1995 ) [7] W.D. Burgess, A. Lashgari and A. Mojiri. Elements of minimal prime ideals in general rings. Advances in Ring Theory, Trends in Mathematics (2010), 69-81. [8] N. J. Divinsky. ”Rings and Radicals”. Mathematical Expositions No. 14 (University of Toronto Press, Toronto 1965 ) [9] E. S. Golod. ”Some ploblems of Burnside type”. (Russian) 1968 Proc. Internet. Congr. Math. (Moskow, 1966), 284-289. [10] B. J. Gardner, R. Wiegandt. ”Radical Theory of Rings”. Chapman & Hall/CRC Pure and Applied Mathematics( Marcel Dekker, Inc. 2003) [11] C. Y. Hong, N. K. Kim, Y. Lee. On LN rings and topological properties of prime spectra. J. Algebra Appl. 15 (2016), 1650102. [12] C. Y. Hong, N. K. Kim, Y. Lee. Near-rings in which each element is a power of itself. Bull. Austral. Math. Soc.2 (1970), 2633-2652. [13] C. Y. Hong, H. K. Kim, N. K. Kim, T. K. Kwak, Y. Lee, and K. S. Park. Rings whose nilpotent elements form a Levitzki radical ring. J. Algebra 35 (2007), no.4, 1379–1390. [14] J. Han, Y. Lee, S. P. Yang. Rings over which polynomial rings are NI. Proc. 6th CJK Conf. Ring theory.(2011). 1-9. [15] S. U. Hwang, Y. C. Jeon, Y. Lee. Structure and topological condition of NI rings. J. Algebra 302 (2006), 186–199. 21 [16] K. Koh. On a representation of a strongly harmonic ring by sheaves. Pacific J. Math 41 (1972), 459–468. [17] N. K. Kim, T. K. Kwak. Minimal prime ideals in 2-primal rings.Math. Japon. 50 (1999), no.3, 415–420. [18] T. Y. Lam, ”A first course in noncommutative rings”. Graduate Texts in Mathematics, 131. Springer-Verlag, (New York, 1991.) [19] J. Lambek. On the representation of modules by sheaves of factor modules. Canad. Math. Bull.14 (1971), 359-368. [20] Y. Lee, C Huh, K. Kim Questions on 2-primal rings. Comm. Algebra. 26(1998). 595-600. [21] G. Marks. On 2-primal Ore extensions. Comm. Algebra 29 (2001), 2113–2123. [22] G. Marks. Skew polynomial rings over 2-primal rings. Comm. Algebra 27(9) (1999), 4411–4423. [23] S. H. Sun. Noncommutative rings in which every prime ideal is contained in a unique maximal ideal. J. Pure Appl. Algebra 76 (1991), no. 2, 179–192. 22 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50794 | - |
| dc.description.abstract | 經由2-primal ring及NI ring的拓撲結構，我們研究一種新的類型的環，滿足所有冪零元形成一個局部冪零理想，並稱之為NL ring。本文首先介紹NL ring的基本性質，接著研究NL ring和局部強質理想之間的關係，最後，探討NL ring下的拓樸結構。 | zh_TW |
| dc.description.abstract | Motivated by 2-primal rings, NI rings and their associated topological structures, we consider a new class of rings, NL rings, in which the nilpotent elements form a locally nilpotent ideal. We first introduce some basic properties of NL rings, and then study the relationships between NL rings and locally strong prime ideals. Lastly, we give the topological structures induced by NL rings. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:58:48Z (GMT). No. of bitstreams: 1 ntu-105-R03221001-1.pdf: 389178 bytes, checksum: 226ce3ef2139aec68876b56217c1b2a1 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 1.Introduction (p.1)
2.Basic Properties of NL rings (p.2) 3.Polynomials over NL rings (p.8) 4.Locally Strong Prime Ideals (p.13) 5.Topological Properties of Prime Spectra (p.19) References (p.26) | |
| dc.language.iso | en | |
| dc.subject | 局部冪零理想 | zh_TW |
| dc.subject | 局部強質理想 | zh_TW |
| dc.subject | NL 環 | zh_TW |
| dc.subject | lspm | zh_TW |
| dc.subject | L 正規 | zh_TW |
| dc.subject | Levitzki radical | zh_TW |
| dc.subject | locally strong prime ideal | en |
| dc.subject | L-normal | en |
| dc.subject | lspm | en |
| dc.subject | locally nilpotent ideal | en |
| dc.subject | Levitzki radical | en |
| dc.subject | NL ring | en |
| dc.title | 冪零元與局部冪零理想 | zh_TW |
| dc.title | On nilpotent elements and locally nilpotent ideals | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡援宗 教授(Yuan-Tsung Tsai),劉承楷(Cheng-Kai Liu) | |
| dc.subject.keyword | 局部冪零理想,Levitzki radical,L 正規,lspm, NL 環,局部強質理想, | zh_TW |
| dc.subject.keyword | locally nilpotent ideal,Levitzki radical,L-normal,lspm,NL ring,locally strong prime ideal, | en |
| dc.relation.page | 27 | |
| dc.identifier.doi | 10.6342/NTU201600882 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-07-13 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-105-1.pdf Restricted Access | 380.06 kB | Adobe PDF |
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