Transfer of Krull Dimension, Lying-Over, and Going-Down to the Fixed Ring

2007 ◽  
Vol 35 (4) ◽  
pp. 1227-1247 ◽  
Author(s):  
David E. Dobbs ◽  
Jay Shapiro
Keyword(s):  
Author(s):  
Stefan Gille

AbstractLet X be a regular noetherian scheme of finite Krull dimension with involution σ and an Azumaya algebra over X with involution τ of the second kind with respect to σ. We construct a hermitian and a skew-hermitian Gersten-Witt complex for (, τ) and show that these complexes are exact if X = Spec R is the spectrum of a regular semilocal ring R of geometric type, such that R is a quadratic étale extension of the fixed ring of σ.


Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1105
Author(s):  
Jianhua Zhao ◽  
Lanchun Xing ◽  
Sheng Li ◽  
Weidong Yan ◽  
Dianrong Gao ◽  
...  

The magnetic-liquid double suspension bearing (MLDSB) is a new type of suspension bearing, with electromagnetic suspension as the main part and hydrostatic supports as the auxiliary part. It can greatly improve the bearing capacity and stiffness of rotor-bearing systems and is suitable for a medium speed, heavy load, and frequent starting occasions. Compared with the active electromagnetic bearing system, the traditional protective bearing device is replaced by the hydrostatic system in MLDSB, and the impact-rubbing phenomenon can be restrained and buffered. Thus, the probability and degree of friction and wear between the rotor and the magnetic pole are reduced drastically when the electromagnetic system fails. In order to explore the difference in the dynamic behavior law of the impact-rubbing phenomenon between the traditional protection device and hydrostatic system, the dynamic equations of the rotor impact-rubbing in three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system) under electromagnetic failure mode are established, and the axial trajectory and motion law of the rotor are numerically simulated. Finally, the dynamic behavior characteristics of the rotor are compared and analyzed. The results show that: Among the three kinds of protection devices (fixed ring/deep groove ball bearing/hydrostatic system), the hydrostatic system has the least influence on bouncing time, impact-rubbing force, and impact-rubbing degree, and the maximum impact-rubbing force of MLDSB is greatly reduced. Therefore, the protective bear is not required to be installed in the MLDSB. This study provides the basis for the theory of the “gap impact-rubbing” of MLDSB under electromagnetic failure, and helps to identify electromagnetic faults.


2011 ◽  
Vol 84 (3) ◽  
pp. 433-440
Author(s):  
A. HAGHANY ◽  
M. MAZROOEI ◽  
M. R. VEDADI

AbstractGeneralizing the concept of right bounded rings, a module MR is called bounded if annR(M/N)≤eRR for all N≤eMR. The module MR is called fully bounded if (M/P) is bounded as a module over R/annR(M/P) for any ℒ2-prime submodule P◃MR. Boundedness and right boundedness are Morita invariant properties. Rings with all modules (fully) bounded are characterized, and it is proved that a ring R is right Artinian if and only if RR has Krull dimension, all R-modules are fully bounded and ideals of R are finitely generated as right ideals. For certain fully bounded ℒ2-Noetherian modules MR, it is shown that the Krull dimension of MR is at most equal to the classical Krull dimension of R when both dimensions exist.


1993 ◽  
Vol 21 (2) ◽  
pp. 705-710
Author(s):  
Robert L. Snider
Keyword(s):  

1992 ◽  
Vol 20 (10) ◽  
pp. 2863-2876 ◽  
Author(s):  
John J. Koker

2016 ◽  
Vol 19 (19) ◽  
pp. 132-132
Author(s):  
David E. Dobbs ◽  
Jay Shapiro
Keyword(s):  

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