On liftable and weakly liftable modules

Let $T$ be a Noetherian ring and $f$ a nonzerodivisor on $T$. We study concrete necessary and sufficient conditions for a module over $R=T/(f)$ to be weakly liftable to $T$, in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over $T$ we define the loci for certain properties: liftable, weakly liftable, having finite projective dimension and study their relationships

Remarks on non-commutative crepant resolutions of complete intersections

We study obstructions to existence of non-commutative crepant resolutions, in the sense of Van den Bergh, over local complete intersections

Characteristics of Vietnamese lexis of Vietnamese Australian immigrants

The Vietnamese of Australian communities (VAC) still maintains many obsolete expressions originating from and related to the Southern Vietnamese political institutions of the pre-1975 Southern government. In addition, VAC has adopted English loanwords (ELs) through close contact with Australian English and uses them extensively to fill gaps in vocabulary. English loanwords have not only been borrowed in their original forms but were also nativized through the mechanism of loanwords and loan translation. Moreover, hybridised expressions have been coined by Vietnamese Australian émigrés through the compounding of one English or Vietnamese item with a Vietnamese or English item through loan blending

A note on Higgs decays into ZZ boson and J/Ψ(Υ)J/\Psi (\Upsilon)

Rare decays $h\to Z V$ with $V$ denoting the narrow $c\bar{c}$ or $b\bar{b}$ resonances, such as $J/\Psi$ or $\Upsilon$ states, have been analyzed. Within the standard model, these channels may proceed through the tree-level transition $h\to ZZ^*$ with the virtual $Z^*\to V$, and also loop-induced process $h\to Z\gamma^*$, followed by $\gamma^*\to V$. Our analysis shows that, for the bottomonium final states, the decay rate of $h\to Z \Upsilon$ from the loop-induced process is small and the former transition gives the dominant contribution; while, for the charmonium final states, $\Gamma(h\to Z J/\Psi)$ and $\Gamma(h\to Z\Psi(2S))$ induced by $h\to Z\gamma^* \to Z V$ could be comparable to the contribution given by the tree-level $h\to ZZ^*\to Z V$ transition.Comment: 6 pages, 2 figure