Some characterizations of regular modules

Let M be a left modula over a ring R. M is called a Zelmanowitz-regular module if for each x Є M there exists a homomorphism f : M → R such that f(x)x = x . Let Q be a left R-module and h : Q → M a homomorphism . We call h locally split if for each x Є M there exists a homomorphism g: M →Q such that h(g(x)) = x . M is called locally projective if every epimorphism onto M is locally split . We prove that the following conditions are equivalent: (1) M is Zelmanowitz-regular. (2) every homomorphism into M is locally split. (3) M is locally projective and every cyclic submodule of M is a direct summand of M

Behavior of countably generated pure-projective modules

We first prove that every countably presented module is a pure epimorphic image of a countably generated pure-projective module, and by using this we show that if every countably generated pure-projective module is pure-injective then every module is pure-injective, while if in any countably generated pure-projective module every countably generated pure-projective pure submodule is a direct summand then every module is pure-projective

Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.The authors are highly grateful to the referee for valuable comments which led to improvements of this paper. In particular, Corollaries 2.5, 2.6 and 3.6, Remarks 2.13 and 3.10 and the final remark (ii) were suggested to the authors by the referee. The first author is grateful to China Scholarship Council for giving him a purse for his further study in University of Minho, Portugal. Jianlong Chen and Huihui Zhu are financed by the National Natural Science Foundation of China (No. 11201063 and No. 11371089), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120092110020), the Natural Science Foundation of Jiangsu Province (No. BK20141327), the Foundation of Graduate Innovation Program of Jiangsu Province(No. CXLX13-072), the Scientific Research Foundation of Graduate School of Southeast University and the Fundamental Research Funds for the Central Universities (No. 22420135011). Pedro Patr´ıcio is financed by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Funda¸c˜ao para a Ciˆencia e a Tecnologia”, through the Project PEst-OE/MAT/UI0013/2014

One-pot synthesis and AFM imaging of a triangular aramide macrocycle

Macrocyclizations in exceptionally good yields were observed during the self-condensation of N-benzylated phenyl p-aminobenzoates in the presence of LiHMDS to yield three-membered cyclic aramides that adopt a triangular shape. An ortho-alkyloxy side chain on the N-benzyl protecting group is necessary for the macrocyclization to occur. Linear polymers are formed exclusively in the absence of this Li-chelating group. A model that explains the lack of formation of other cyclic congeners and the demand for an N-(o-alkoxybenzyl) protecting group is provided on the basis of DFT calculations. High-resolution AFM imaging of the prepared molecular triangles on a calcite(10.4) surface shows individual molecules arranged in groups of four due to strong surface templating effects and hydrogen bonding between the molecular triangles

N-(2,3-Dimethyl­phen­yl)benzamide

The conformation of the N—H bond in the structure of the title compound, C15H15NO, is anti to the ortho and meta-methyl substituents in the aniline benzene ring, in contrast to the syn conformation observed with respect to the ortho and meta-chloro substituents in N-(2,3-dichloro­phen­yl)benzamide. Furthermore, the conformations of N—H and C=O bonds in the amide group are anti to each other, similar to those observed in other benzanilides. The dihedral angle between the benzoyl and aniline rings is 84.1 (2)°. The amide group is twisted by 23.0 (3)° out of the plane of the benzoyl ring. The structure exhibits positional disorder over the aniline ring, with site occupancies of 0.80 (1) and 0.20 (1) for the major and minor components, respectively. In the crystal, mol­ecules are connected through N—H⋯O hydrogen bonds into chains running along the b axis. An intra­molecular C—H⋯O close contact occurs

Extension groups between atoms and objects in locally noetherian Grothendieck category

We define the extension group between an atom and an object in a locally noetherian Grothendieck category as a module over a skew field. We show that the dimension of the i-th extension group between an atom and an object coincides with the i-th Bass number of the object with respect to the atom. As an application, we give a bijection between the E-stable subcategories closed under arbitrary direct sums and direct summands and the subsets of the atom spectrum and show that such subcategories are also closed under extensions, kernels of epimorphisms, and cokernels of monomorphisms. We show some relationships to the theory of prime ideals in the case of noetherian algebras.Comment: 18 page

Adapting Ferritin, a Naturally Occurring Protein Cage, to Modulate Intrinsic Agonism of OX40

Ferritin is a multivalent, self-assembling protein scaffold found in most human cell types, in addition to being present in invertebrates, higher plants, fungi, and bacteria, that offers an attractive alternative to polymer-based drug delivery systems (DDS). In this study, the utility of the ferritin cage as a DDS was demonstrated within the context of T cell agonism for tumor killing. Members of the tumor necrosis factor receptor superfamily (TNFRSF) are attractive targets for the development of anticancer therapeutics. These receptors are endogenously activated by trimeric ligands that occur in transmembrane or soluble forms, and oligomerization and cell-surface anchoring have been shown to be essential aspects of the targeted agonism of this receptor class. Here, we demonstrated that the ferritin cage could be easily tailored for multivalent display of anti-OX40 antibody fragments on its surface and determined that these arrays are capable of pathway activation through cell-surface clustering. Together, these results confirm the utility, versatility, and developability of ferritin as a DDS

Growth variation in long blade kelp Saccharina longissima in eastern Hokkaido, Japan

Saccharina longissima (Naga-konbu in Japanese) is distributed in shallow Pacific coastal areas from eastern Hokkaido (Kushiro and Nemuro) to Chishima Island. It is a commercially important Laminariacean kelp species in this area. The variations in the blade size of S. longissima (age 1+) were analyzed in Habomai, eastern Hokkaido, Japan. The fisheries cooperative association of Habomai in Nemuro monitored the blade size of the kelp in the harvest grounds along more than 15 km of coastline in May and June from 2000 to 2014. The monitoring data showed that the blade weight varied among years, and the growth of blade weight was greater in 2002 and 2009 then the other years. The kelps had a poorer growth of the blade in 2001, 2011 and 2013. Correlation analysis revealed that the coefficients between the blade weight in May and the monthly mean water temperature in spring to autumn in the previous year were negative but positive in winter to spring in the same year. Generalized linear regression model (GLM) analysis of the blade weight in May also revealed that the growth models including only monthly mean water temperature (January, April, July and October in the previous year, January, April during in the same year) and longitude effectively estimated the variation of the annual mean weight. Correlation analysis also revealed that the mean wet weight of S. longissima in May represents the growth condition of the kelp of the year, and it is useful for predicting the annual fisheries production in this area. These results suggested that the weight growth of S. longissima is affected by the ambient water temperature both in the previous and the same years. High temperature in the preceding autumn and extremely low temperature in the preceding winter to spring reduce the blade weight in the summer harvest season. Therefore, the increasing trends of water temperature in recent years may be one of the factors decreasing the fisheries production of the kelp in eastern Hokkaido.departmental bulletin pape