UP整环上的u-平坦模

发布时间：2018-07-12 20:33

  本文选题：UP整环 + u-模　； 参考：《四川师范大学学报(自然科学版)》2017年06期

【摘要】：设R是UP整环.R-模M是u-平坦模,是指对任意u-单同态f:A→B,使得1懔f:M懔_RA→M懔_RB是u-单同态.建立懔函子上的u-长正合列,证明R-模M是u-平坦模当且仅当对任何u-正合列0→A→B→C→0,序列0→M懔_RA→M懔_RB→M懔_RC→0是u-正合列,当且仅当对R的任何极大u-理想m,M_m是平坦R_m-模,当且仅当对R的任何理想I,自然同态M懔_RI→IM是u-同构.最后证明若{A_i|i∈Γ}是M的u-平坦子模的正向系,其中Γ是定向集,则lim→Ai是u-平坦模.
[Abstract]:Let R be a up integral ring. R-module M is a u-flat module, which means that for any u-single homomorphism f: a / B, let 1 be apprehensive of F: M apprehensive of RA / M apprehensive of S / M / RB is u-monomorphism. Establishing the u-long positive sequence on apprehensive functors, proving that R-module M is u-flat if and only if for any u-positive train 0 A / B / C / 0, sequence 0 / M apprise RA / M / RB / M / S / S / R / M / S / S / M / S / S / M / S / M / S / M / M / S / M / S / M / S / M / S / M / S / M / S / M / S / M If and only if any maximal u- ideal M _ m of R is a flat Rms-norm, and if and only if for any ideal I of R, the natural homomorphism M apprise RI _ I _ IM is u-isomorphism. Finally, it is proved that if {A _ I _ I 鈭，

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