A sectionally complemented modular lattice L is coordinatizable if it is isomorphic to the lattice L(R) of all principal right ideals of a von Neumann regular (not necessarily unital) ring R. We say that L has a large 4-frame if it has a homogeneous sequence (a0, a1, a2, a3) such that the neutral ideal generated by a0 is L. Jónsson proved in 1962 that if L has a countable cofinal sequence and a...

Let Io and m° be the ideals associated with Laver and Miller forcing, respectively. We show that add(/°) < cov(/°) and add(m°) < cov(m°) are consistent. We also show that both Laver and Miller forcing collapse the continuum to a cardinal < f). Introduction and notation In this paper we investigate the ideals connected with the classical tree forcings introduced by Laver [La] and Miller [Mi]. La...

The micellar and surface behaviors of decylammonium chloride (DACl) in presence L-alanine hydrochloride decylester (L-ADE) dodecylester (L-ADDE) at various mole fractions were investigated by conductivity tension measurements. From the measurements, critical micelle concentration (CMC), degree counter-ion ionization (α) standard Gibbs energy micellization (ΔG°mic) for both pure binary mixtures....

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

Theorem 1.1. Let A be a semisimple complex Banach algebra with the following properties: (i) for every closed right ideal R in A, there exists a closed left ideal L such that R∩L= {0} and R+ L= A (each a∈ A can be written in the form a= a1 + a2 with a1 ∈ R, a2 ∈ L); (ii) if a,b in A are such that ab = ba= 0, then ‖a+ b‖2 = ‖a‖2 +‖b‖2. Then A is a commutative proper H∗-algebra [1]. It is easy to...