In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

Here V is the tangent to M and A is the tangent to ∂M . (By the tangent, we mean, e.g., that V (X) is the unit positively oriented pseudoscalar in the tangent algebra to M at X.) Recall the important relationship V A = N , where N is the unit outward normal to M [4, p. 319]. The relationships dV = |dV |V and dA = |dA|A define the integrals componentwise as Lebesgue integrals on M and ∂M [4, p. ...

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

BACKGROUND Although exposure to second-hand smoke (SHS) has been associated with various medical conditions, only limited data are available on its association with health-related quality of life (HRQOL), particularly data obtained with the EQ-5D or EQ visual analogue scale (VAS). METHODS This cross-sectional study evaluated 10,532 adult never-smokers who participated in the fifth Korea Natio...

this paper provides a review on major ergodic features of semi-independent hyper mv {algebra dynamical systems. theorems are presentedto make contribution to calculate the entropy. particularly, it is proved that thetotal entropy of those semi-independent hyper mv {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

INTRODUCTION The new, five-level version of the EQ-5D (EQ-5D-5L) questionnaire has better psychometric properties than the standard three-level version (EQ-5D-3L), including a reduced ceiling effect. Currently, there are few existing population norms for the EQ-5D-5L. The aims of this study were to provide population norms for the EQ-5D-5L in Poland, based on a representative sample of adults, ...

BACKGROUND The EQ-5D is a brief, generic measure of health status that can be easily incorporated into population health surveys. There are two versions of the EQ-5D for use in adult populations, one with 3 response levels in each of the instrument's 5 dimensions (EQ-5D-3L) and one with 5 levels in each dimension (EQ-5D-5L). We compared the two versions as measures of self-reported health statu...