Coincidence of topological Jacobson radicals in topological algebras

Several classes of topological algebras for which the left topological Jacobson radical coincides with the right topological Jacobson radical are described

Ford Lemma for topological ∗-algebras

Abstract. Several analogies of Ford lemma for topological algebras (in particular, for topological *-algebras) are proved (without using projective limits). Topological *-algebras, in which a self-adjoint element a with sp A (a) ⊂ (0, ∞) has a self-adjoint square root b with sp A (a) ⊂ (0, ∞) and sp Key words: advertive algebras, Ford lemma, Gelfand-Mazur algebras, locally pseudoconvex algebras, simplicial algebras, square root of an element, topological *-algebras. At several places in the development of the theory of topological *-algebras (especially, of the theory of Banach *-algebras and locally m-convex *-algebras) a self-adjoint square root for a self-adjoint element with a positive spectrum is needed. I

The center of topologically primitive exponentially galbed algebras

Let A be a unital sequentially complete topologically primitive exponentially galbed Hausdorff algebra over ℂ, in which all elements are bounded. It is shown that the center of A is topologically isomorphic to ℂ

Primers auxilis 2021

Els primers auxilis (PA) són l'atenció inicial prestada en cas de malaltia aguda o lesió que es presenta de manera sobtada, i que pot ser iniciada per qualsevol persona (proveïdor) en qualsevol situació incloent-hi l'autocura. Els objectius dels primers auxilis són preservar la vida, alleujar el patiment, prevenir noves malalties o lesions i promoure la recuperació. Les primeres guies del Consell Europeu de Ressuscitació (ERC) sobre PA van aparèixer l'any 2015, i el Comitè d'RCP de la Societat Catalana de Pediatria (CRCPSCP) les va difondre a través de Pediatria Catalana. En aquell article es donava també a conèixer la història del desenvolupament dels PA. El canvi que ha significat la introducció del concepte de suport vital ha comportat que els últims anys els PA siguin considerats un tema important també per als professionals sanitaris. En aquest sentit, les guies pediàtriques ERC 2021 ressalten la importància que té la identificació i el maneig precoç de l'infant críticament malalt o lesionat i el coneixement que en tinguin els proveïdors de PA. En aquest informe es presenten les recomanacions 2021 de l'ERC referents als PA, sobre la base de la revisió de l'ILCOR, amb vint temes relacionats amb emergències, mèdiques i traumàtique

Dense subalgebras in noncommutative Jordan topological algebras

Wilansky conjectured in [12] that normed dense Q-algebras are full subalgebras of Banach algebras. Beddaa and  Oudadess proved in [2] that Wilansky’s conjecture was true. They showed that k-normed Q-algebras are full subalgebras of k-Banach algebras for each k∈(0,1]. Moreover, J. Pérez, L. Rico and A. Rodríguez showed in [8], Theorem 4, that this was also true in the case of noncommutative Jordan-Banach algebras. In the present paper this problem has been studied in a more general case. It is proved that all dense Q-subalgebras of topological algebras and of noncommutative Jordan topological algebras with continuous multiplication are full subalgebras. Some equivalent conditions that a dense subalgebra would be a Q-algebra (in subspace topology) in Q-algebras and in nonassociative Jordan Q-algebras with continuous multiplication are given

On a problem of Bertram Yood

In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide

Real Gel'fand-Mazur division algebras

We show that the complexification (A˜,τ˜) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (A˜,τ˜) of a commutative real exponentially galbed algebra (A,τ) with bounded elements are bounded if the multiplication in (A,τ) is jointly continuous. We give conditions for a commutative strictly real topological division algebra to be a commutative real Gel'fand-Mazur division algebra