Let R be a universally catenary locally equidimensional Noetherian ring. We give a multiplicity based criterion for an arbitrary finitely generated R-module to be integral over a submodule. Our proof is self-contained and implies the previously known numerical criteria for integral dependence of ideals and modules.

We show that group algebras kG of polycyclic-by-finite groups G, where k is a field, are catenary: If P = I0 I1 · · · Im = P ′ and P = J0 J2 · · · Jn = P ′ are both saturated chains of prime ideals of kG, then m = n.

Krassimir Atanassov1, Gabriella Pasi2, Ronald Yager3, and Vassia Atanassova4 1 CLBME Bulg. Academy of Sci., P.O.Box 12, Sofia-1113, Bulgaria, [email protected] 2 ITC-CNR, Via Ampère 56, 20131 Milano, Italy, [email protected] 3 Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA, [email protected] 4 Faculty of Mathematics and Computer Science, Sofia University, V assia...

Top-and-seat angle connections are a conventional type of steel moment connection. However, their capacity in accommodating columns loss is rarely studied. In this study, five multistory subframes using top-and-seat were fabricated and tested to investigate performance while subjected various column-removal scenarios, including: (1) middle column loss, (2) penultimate (3) corner loss. Moreover,...

When a train runs at high speed, affected by the structural characteristics of catenary, contact force changes periodically with span and dropper spacing. However, as running speed increases, periodic signal owing to fluctuation catenary vibration pantograph, which directly affects stable between pantograph catenary. Therefore, based on simulation research method, this study uses time–frequency...