A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...

We introduce the notion of weakly (strongly) infinite real rank for unital C∗-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C∗-algebra C∗ (F∞) of the free group on countable number of generators ha...

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in spaces over metric may be reduced to the same free their compact subsets. As easy consequences we derive several new and some known results. The main results are: $\mathcal F(X)$ is sequentially complete for every superreflexive Banach space $X$...

In the present paper‎, ‎we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$‎. ‎We also define the concept of weakly related mappings on an ordered space‎. ‎Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space‎.

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

In this paper, spaces with σ-locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or g-first countable spaces with σ-locally countable cs-networks). To find the internal characterizations of certain images of metric spaces is an interesting research topic on general topology. Recently, S. Xia introduced the concept of weakly open mappings, by using it,...

In the title complex, {[Cu(C(11)H(8)N(2)O)(2)](BF(4))(2)}(n), the Cu(II) ion is situated on an inversion centre and adopts an N(4)F(2) octa-hedral coordination geometry with four N atoms from four different bis-(pyridin-3-yl)methanone ligands at the equatorial sites and two independent tetra-fluoridoborate anions weakly bonded at the axial sites via two F atoms [Cu⋯F = 2.613 (3) Å]. Chains with...

The F(2)+CH(3)SCH(3) reaction was studied with crossed molecular beam techniques and high level ab initio calculations. Significant reactivity was observed even at low collision energies, consistent with the negligible barrier height obtained from the ab initio calculations. All experimental findings are consistent with a weakly bound reaction intermediate of F-F-S(CH(3))(2) structure, which po...

Melt produced by friction during earthquakes may act either as a coseismic fault lubricant or as a viscous brake. Here we estimate the dynamic shear resistance (tau(f)) in the presence of friction-induced melts from both exhumed faults and high-velocity (1.28 meters per second) frictional experiments. Exhumed faults within granitoids (tonalites) indicate low tau(f) at 10 kilometers in depth. Fr...