多项式环的表现维数
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摘要
设R为有单位元的环,M为右R-模,通过研究多项式环上的表现维数,得到了当R,R[x]为凝聚环时,MR与MR[x]的表现维数之间的关系以及R与R[x]的表现维数之间的关系等结论。
Let R be a ring with a unit element,and M be a right R-M odule. The relationship between FPd( MR) and FPd( MR[x]) as well as between FPD( R) and FPD( R[x]) are obtained by using the presented dimensions of polynomial rings,when R and R[x] are coherent rings.
Let R be a ring with a unit element,and M be a right R-M odule. The relationship between FPd( MR) and FPd( MR[x]) as well as between FPD( R) and FPD( R[x]) are obtained by using the presented dimensions of polynomial rings,when R and R[x] are coherent rings.
引文
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[3]ZHOU Dexu,GONG Zhiwei.On presented dimensions of modules and rings[J].International Journal of Mathematics and M athematical Sciences,2010:1-13.doi:10.1155/2010/256267.
[4]李元林.有限表现维数的换环定理[J].南京大学学报:数学半年刊,1990,7(1):75-84.LI Yuanlin.Some theorems on chane of rings of the finitely presented dimension[J].Journal of Nanjing University M athematical Biquarterly,1990,7(1):75-84.
[5]周伯壎.同调代数[M].北京:科学出版社,1988.ZHOU Boxun.Homological algebra[M].Beijing:Science Press,1988.
[6]程福长,易忠.环的同调维数[M].桂林:广西师范大学出版社,2000.CHENG Fuchang,YI Zhong.Homological dimension of rings[M].Guilin:Guangxi Normal University Press,2000.
[7]李元林.F.P.-维数的合冲定理[J].数学研究与评论,1993,13(2):283-288.LI Yuanlin.Syzygy theory of F.P.-dimension[J].Journal of M athematical Research and Exposition,1993,13(2):283-288.