In this paper we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion passport Γ(X) for faithful Amodules X, which consist uniquely defined partition unity in Boolean algebra all idempotents and set pairwise different cardinal numbers. prove that A-modules X Y are isomorphic if only = Γ(Y). Further Banach case C∞(Q) or C∞(Q)+i ...

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

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 $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...

Generalizing a concept of Lipshitz, Ozsváth and Thurston from Bordered Floer homology, we define D-structures on algebras of unital operads. This construction gives rise to an equivalence of derived categories, which can be thought of as a unital version of Koszul duality using non-unital Quillen homology, even though the non-unital Quillen homology of unital objects is zero.

Let A be a C∗-algebra. Let E and F be Hilbert A-modules with E being full. Suppose that θ : E → F is a linear map preserving orthogonality, i.e., 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We show in this article that if, in addition, A has real rank zero, and θ is an A-module map (not assumed to be bounded), then there exists a central positive multiplier u ∈M(A) such that 〈θ(x), θ(y)〉 = u〈x, y〉 (x...

We present a general approach to a module frame theory in C∗algebras and Hilbert C∗-modules. The investigations rely on the ideas of geometric dilation to standard Hilbert C∗-modules over unital C∗-algebras that possess orthonormal Hilbert bases, of reconstruction of the frames by projections and by other bounded module operators with suitable ranges. We obtain frame representation and decompos...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space