In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

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, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

BL-algebras have been invented by P. Hájek [3] in order to provide an algebraic proof of the completeness theorem of “Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The above notion is generalized to an algebraic system in which the required conditions are fulfilled (Definition 2.1). Filters in BL-algebras are also defined. A fi...

We show that, if A is a finite-dimensional *-simple associative algebra with involution (over the field K of real or complex numbers) whose hermitian part H( A, * > is of degree > 3 over its center, if B is a unital algebra with involution over 06, and if (I.11 is an algebra norm on H( A @ B, * 1, then there exists an algebra norm on A @ B whose restriction to H(A @ B, *> is equivalent to 11 . ...

Let K be an infinite compact space, let C(K) be the algebra of continuous complex-valued functions of K, let F be a well-ordered chain of nonmaximal prime ideals of C(K), let IF be the smallest element of F and let MF be the unique maximal ideal of C(K) containing the elements of F . Assuming the continuum hypothesis, we show that if |C(K)/IF | = 20 , and if there exists a sequence (Gn)n≥1 of s...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

* The work reported in this note was done while the author was a fellow of the John Simon Guggenheim Memorial Foundation on leave of absence from the University of Brazil, Rio de Janeiro. This work was sponsored in part by the Army Algebras Research Project No. 2 at the University of Chicago. 1 All algebras considered here are supposed to be commutative, with unit, over the field of real number...

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.