We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...

Let δ be a nondegenerate coaction of G on a C∗-algebra B, and let H be a closed subgroup of G. The dual action δ̂ : H → Aut(B×δ G) is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the crossed product of B by the homogeneous space G/H . The resulting Morita equivalence is a version of Mansfield’s imprimitivity theorem which requires neither amenability n...

The connection between doubly transitive permutation groups G on a finite set Cl which are not doubly primitive and automorphism groups of block designs in which X = 1 has been investigated by Sims [2] and Atkinson [1]. If, for a e Q, Ga has a set of imprimitivity of size 2 then it is easy to show that G is either sharply doubly transitive or is a group of automorphisms of a non-trivial block d...

In this paper we effect a systematic study of transitive subgroups of M24, obtaining 5 transitive maximal subgroups of M24 of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of M2i. I, enable us to enumerate all the maximal subgroups of M24. There are, up to conjugacy, nine of them. The complete list includes one more in addition to ...

Let U be a (B, A)-bimodule, A and B rings, formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using left global dimensions B, estimate dimension T-module.

In this section we shall assume that all algebras are finite dimensional algebras over an algebraically closed field F. The fact that F is algebraically closed is only for convenience, to avoid the division rings that could arise in the decomposition of Ā just before (4.8) below. Let A ⊆ B be an inclusion of algebras. Then B⊗F B is an (A,A)-bimodule where A acts on the left by left multiplicati...

Let A be a unital Banach algebra. We give a characterization of the left Banach A-modules X for which there exists a commutative unital C-algebra C(K), a linear isometry i:X → C(K), and a contractive unital homomorphism θ:A → C(K) such that i(a· x) = θ(a)i(x) for any a ∈ A, x ∈ X . We then deduce a “commutative” version of the Christensen-Effros-Sinclair characterization of operator bimodules. ...

Mackey’s imprimitivity theorem characterises the unitary representations of a locally compact group G which have been induced from representations of a closed subgroupK; Rieffel’s influential reformulation says that the group C-algebra C(K) is Morita equivalent to the crossed product C0(G/K) × G [14]. There have since been many important generalisations of this theorem, especially by Rieffel [1...

In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã. 2000 Mathematics Subject Classification : 16E40