In the present paper we give a self-contained proof of Imprimitivity theorem for systems of covariance, or generalised imprimitivity systems, based on transitive spaces. The theorem holds for locally compact groups and non-normalised positive operator valued (POV) measures. For projective valued measures, the theorem was proven by Mackey, [21], for separable groups, and by Blattner, [4], in ful...

Let $T=\biggl(\begin{matrix} A&0\\U&B\end{matrix}\biggr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We first give some computing formulas of projective, injective, flat $FP$-injective dimensions special left $T$-modules. Then we establish (weak) global $T$. It proven that (1) If $U_{A}$ $_{B}U$ $lD(A)\neq lD(B)$, then $lD(T)={\rm m...

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...

We show how to extend a classic Morita Equivalence Result of Green’s to the C∗-algebras of Fell bundles over transitive groupoids. Specifically, we show that if p : B → G is a saturated Fell bundle over a transitive groupoid G with stability group H = G(u) at u ∈ G(0), then C∗(G,B) is Morita equivalent to C∗(H,C ), where C = B|H . As an application, we show that if p : B → G is a Fell bundle ov...

in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis

Given C-algebras A and B acting cyclically on Hilbert spaces H and K, respectively, we characterize completely isometric A, B-bimodule maps from B(K,H) into operator A, B-bimodules. We determine cogenerators in some classes of operator bimodules. For an injective cogenerator X in a suitable category of operator A, B-bimodules we show: if A, regarded as a Csubalgebra of Al(X) (adjointable left m...

We give an algorithmic way to construct a free bimodule resolution of an algebra admitting a Gröbner base. It enables us to compute the Hochschild (co)homology of the algebra. Let A be a finitely generated algebra over a commutative ring K with a (possibly infinite) Gröbner base G on a free algebra F , that is, A is the quotient F/I(G) with the ideal I(G) of F generated by G. Given a Gröbner ba...

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis