Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

First principles investigations of Fe,Co, Ni in model honeycomb carbon networks

The behaviors of ferromagnetic transition metals of the first period: Fe, Co and Ni are examined within density functional theory calculations in two dimensional carbon extended networks using model structure LiC₆. Around geometry optimized structures, the energy-volume equations of states considering non magnetic and spin polarized configurations established ferromagnetic ground states with magnetizations –reduced with respect to the metals’– of 2 μ_B for FeC₆ and 1 μ_B for CoC₆ while no magnetic solution could be identified for NiC₆. In the D_6h point group of the P6/mmm space group l_m decomposition of the d states results with increasing energy into doublet state E_1g with d(x²-y²) and d(xy); singlet state A_1g d(z²) and doublet state E_2g d(xz) and d(yz) lying on E_F and responsible of the onset of magnetic moments. This was mirrored via molecular orbital approach with a construct of Fe embedded between two extended carbon networks thus validating the model structure proposed for TC₆ compounds. The 100% polarization in one spin channel allows proposing potential uses in spintronics applications.     

Chase’s lemma and its context

Chase’s lemma provides a powerful tool for translating properties of (co)products in abelian categories into chain conditions. This note discusses the context in which the lemma is used, making explicit what is often neglected in the literature because of its technical nature.     

偏缠绕模的Frobenius性质

主要给出了偏缠绕模的Frobenius性质，推广了缠绕模相应的性质。     

An Upper Bound for the w-Weak Global Dimension of Pullbacks

Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}.