After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

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, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

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.

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...