Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

Consider a bounded strongly pseudo-convex domain Ω with smooth boundary in Cn. Let T be the Toeplitz algebra on Bergman space La2(Ω). That is, is C⁎-algebra generated by operators {Tf:f∈L∞(Ω)}. Extending work [27], [28] special case of unit ball, we show that any such Ω, and {Tf:f∈VObdd}+K are essential commutants each other, where K collection compact On general considered this paper, proofs r...

In this paper, we deal with the invertible elements in a complete intuitionistic fuzzy pseudo normed algebra (in short, IFPNA) respect to Archimedean t-norm and t-conorm. It is done by studying continuity of algebraic operations IFPNA investigating condition for existence inverse an element IFPNA. Also some properties are studied. observed that set open set.

In a recent paper pair of operators $a$ and $b$ satisfying the equations $a^\dagger a=bb^\dagger+\gamma\1$ $aa^\dagger=b^\dagger b+\delta\1$, has been considered, their nature ladder deduced analysed. Here, motivated by spreading interest in non self-adjoint Quantum Mechanics, we extend this situation to set four operators, $c$, $d$, $r$ $s$, $ dc=rs+\gamma\1$ $cd=sr+\delta\1$, show that they a...

In this paper we find a field such that the algebras obtained by the Cayley-Dickson process are division algebras of dimension 2t,∀t ∈ N. Subject Classification: 17D05; 17D99. From Frobenius Theorem and from the remark given by Bott and Milnor in 1958, we know that for n ∈ {1, 2, 4} we find the real division algebras over the real field R. These are: R, C, H(the real quaternion algebra), O(the ...

New invariants of 3-dimensional manifolds appearing in the Ktheory of certain operator algebras are introduced. First, we consider the conjugacy problem for pseudo-Anosov diffeomorphisms of a compact surface X. The operator algebra in question is an AF -algebra attached to stable (unstable) foliation of the pseudo-Anosov diffeomorphism. We prove that conjugacy classes of commensurable pseudoAno...