‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

If the free algebra F on one generator in a variety V of algebras (in the sense of universal algebra) has a subalgebra free on two generators, must it also have a subalgebra free on three generators? In general, no; but yes if F generates the variety V. Generalizing the argument, it is shown that if we are given an algebra and subalgebras, A0 ⊇ · · · ⊇ An, in a prevariety (S P -closed class of ...

In this paper the notion of fuzzy dot BCK-subalgebra is introduced. We state and prove some theorem in fuzzy dot BCK-subalgebra and level subalgebras. Mathematics Subject Classification: 06F35, 03G25, 94D05

In this paper we examine subalgebras on two generators in the univariate polynomial ring. A set, S, of polynomials in a subalgebra of a polynomial ring is called a canonical basis (also referred to as SAGBI basis) for the subalgebra if all lead monomials in the subalgebra are products of lead monomials of polynomials in S. In this paper we prove that a pair of polynomials {f, g} is a canonical ...

A completion procedure for computing a canonical basis for a k-subalgebra is proposed. Using this canonical basis, the membership problem for a k-subalgebra can be solved. The approach follows Buchberger's approach for computing a Grr obner basis for a polynomial ideal and is based on rewriting concepts. A canonical basis produced by the completion procedure shares many properties of a Grr obne...

Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something that can be called a descent algebra. There is also a commutative, semisimple subalgebra of Solomon’s descent algebra generated by sums of permutations with the sam...

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group Fr, 2 ≤ r ≤ ∞, on a probability ...

Let L be a Lie pseudoalgebra, a ∈ L. We show that, if a generates a (finite) solvable subalgebra S = 〈a〉 ⊂ L, then one may find a lifting ā ∈ S of [a] ∈ S/S such that 〈ā〉 is nilpotent. We then apply this result towards vertex algebras: we show that every finite vertex algebra V admits a decomposition into a semi-direct product V = U⋉N , where U is a subalgebra of V whose underlying Lie conforma...

The theory of “subalgebra basis” analogous to standard basis (the generalization of Gröbner bases to monomial ordering which are not necessarily well ordering [1].) for ideals in polynomial rings over a field is developed. We call these bases “SASBI Basis” for “Subalgebra Analogue to Standard Basis for Ideals”. The case of global orderings, here they are called “SAGBI Basis” for “Subalgebra Ana...

In this article, we proved the following results. Let L(F (ni)) be the free group factor on ni generators and λ(gi) be one of standard generators of L(F (ni)) for 1 ≤ i ≤ N . Let Ai be the abelian von Neumann subalgebra of L(F (ni)) generated by λ(gi). Then the abelian von Neumann subalgebra ⊗i=1Ai is a maximal injective von Neumann subalgebra of ⊗i=1L(F (ni)). When N is equal to infinity, we o...