We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h A labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Mori...

In this paper, we set up the bi-module of the algebra A on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are investigated in various physical systems. PACS Numbers: 46.10.+z, 05.40.+j, 05.60.+w

We introduce the dimension matrix of a bimodule complex and trace chain endomorphism complex, give Hirzebruch-Riemann-Roch (HRR) Lefschetz type formulas for finite dimensional elementary algebras global dimension. Moreover, we compare our HRR with Shklyarov's Petit's dg algebras.

Let A be a unital R-algebra and M be a unital A-bimodule. It is shown that every Jordan derivation of the trivial extension of A by M, under some conditions, is the sum of a derivation and an antiderivation.

let a be a banach algebra and x be a banach a-bimodule. in this paper, we dene a new product on a  x and generalize the module extension banach algebras. we obtain characterizations of arens regularity, commutativity, semisimplity, and study the ideal structure and derivations of this new banach algebra.