Three results for $\tau $-rigid modules

Rigid Mixin Modules

RESULTS ON ALMOST COHEN-MACAULAY MODULES

Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.

Three Crossed Modules

In this paper following Conduché’s, [12], way of defining 2-crossed modules which are equivalent to Carrasco-Cegarra’s, [10], 2-hyper crossed complexes, we define the three crossed module of groups as a model for 4-types.

New Results for Time-Optimal Three-Axis Reorientation of a Rigid Spacecraft

Some new results for a classical minimum time, rest-to-rest maneuver problem are presented. An inertially symmetric rigid body is considered. For the case that the magnitude of the control is constrained while the control direction is left free, we analytically prove that the eigenaxis maneuver is the time minimum solution by using the Pontryagin’s principle. For the case that the three compone...

An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i.e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)