对偶数环导出范畴的Recollements

(1. 龙岩学院信息工程学院,福建 龙岩 364012; 2. 福建师范大学数学与计算机科学学院,福建 福州 350117)

对偶数环; 导出范畴; recollements

Recollements of Derived Categories of Rings of Dual Numbers
LIU Hongjin1,2*,CHEN Qinghua2

(1.School of Information Engineering,Longyan University,Longyan 364012,China; 2.College of Mathematics and Computer Science,Fujian Normal University,Fuzhou 350117,China)

dual numbers rings; derived categories; recollements

DOI: 10.6043/j.issn.0438-0479.201803065

备注

设A,A1和A2是环.证明若环A的上有界导出范畴D-(A)允许有关于环A1和A2的上有界导出范畴D-(A1)和D-(A2)的recollement,则A的对偶数环A[ε]的上有界导出范畴D-(A[ε])允许有关于A1的对偶数环的上有界导出范畴D-(A1[ε])和A2的对偶数环的上有界导出范畴D-(A2[ε])的recollement.

Let A,A1 and A2 be rings.It is proved that,if the upper bounded derived module category D-(A-Mod)admits a recollement relative to D-(A1-Mod)and D-(A2-Mod),then D-(A[ε]-Mod)admits a recollement relative to D-(A1[ε]-Mod)and D-(A2[ε]-Mod),where A[ε] is the ring of dual number of ring A.