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OALib Journal期刊
ISSN: 2333-9721
费用：99美元
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广义最大公因子整环中的*-理想
, PP. 14-17
Keywords: GGCD整环,*-理想,*-乘法封闭的,多项式环
Abstract:
主要对GGCD整环中的w-理想与t-理想进行了研究,并讨论了GGCD整环与PVMD之间的联系.证明了R是GGCD整环当且仅当R是w-乘法封闭的PVMD,当且仅当R是t-乘法封闭的PVMD.此外,利用星型算子理论给出了GGCD整环与其多项式环及分式环之间的一些等价刻画.
| [1] | 王芳贵. 交换环与星型算子理论[M]. 北京:科学出版社,2006.
|
| [2] | Gilmer R. Multiplicative Ideal Theory[M]. New York:Marcel Dekker,1972.
|
| [3] | 王芳贵. 星型算子理论的发展及其应用[J]. 四川师范大学学报:自然科学版,2009,32(2):249-259.
|
| [4] | 王芳贵. 有限表现型模和w-凝聚环[J]. 四川师范大学学报:自然科学版,2010,33(1):1-9.
|
| [5] | Anderson D D. π-domains, overrings, and divisorial ideals[J]. Glasgow Math J,1978,19:199-203.
|
| [6] | Anderson D D, Anderson D F. Generalized GCD domains[J]. Comment Math Univ St Pauli,1979,28:215-221.
|
| [7] | Anderson D D, Anderson D F, Markanda R. The rings R(X) and R〈X〉[J]. J Algebra,1985,95:96-115.
|
| [8] | Zafrullah M. On a property of pre-Schreier domains[J]. Commun Algebra,1987,15:1895-1920.
|
| [9] | Bouvier A, Zafrullah M. On some class groups of an integral domain[J]. Bull Math Soc,1988,29:45-49.
|
| [10] | Zafrullah M. Flatness and invertibility of an ideal[J]. Commun Algebra,1990,18:2151-2158.
|
| [11] | Fontana M, Gabelli S. On the class group and the local class group of a pullback[J]. J Algebra,1996,181:803-835.
|
| [12] | Kim H, Kwon T I, Park Y S. Factorization and divisibility in generalized Rees rings[J]. Bull Korean Math Soc,2004,41:473-482.
|
| [13] | Anderson D D, Dumitrescu T, Zafrullah M. Quasi-Schreier domains II[J]. Commun Algebra,2007,35:2096-2104.
|
| [14] | Kim H. Module-theoretic characterizations of generalized GCD domains[J]. Commun Algebra,2010,38:759-772.
|
| [15] | Zafrullah M. On generalized Dedekind domains[J]. Mathematika,1986,33:285-295.
|
| [16] | 陈幼华,尹华玉. 两类整环在w-算子下的刻画[J]. 数学学报,2010,53(4):685-690.
|
| [17] | Wang F G. w-modules over a PVMD[M]. Hong Kong:Proc ISTAEM,2001:117-120.
|
| [18] | Anderson D D. Star-operations induced by overrings[J]. Commun Algebra,1988,16:2535-2553.
|
| [19] | Kang B G. Prüfer v-multiplication domains and the ring R[X]Nv[J]. J Algebra,1989,123:151-170.
|
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