Abstract We prove a strengthened version of Shavrukov’s result on the non-isomorphism diagonalizable algebras two $\Sigma _1$ -sound theories, based improvements previously found by Adamsson. then obtain several corollaries to applying it various pairs theories and new examples. In particular, we show that there are no surjective homomorphisms from algebra $(\mathfrak {L}_T, \Box _T\Box _T)$ on...

In this paper, we introduce the following additive type functional equation f(rx+ sy) = r + s 2 f(x+ y) + r − s 2 f(x− y), where r, s ∈ R with r + s, r − s 6= 0. Also we investigate the Hyers–Ulam–Rassias stability of this functional equation in Banach modules over a unital C∗-algebra. These results are applied to investigate homomorphisms between C∗-algebras. 2000 Mathematics Subject Classific...

The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN . For each M = 1 ,2 , . . . denote by A M N the centralizer of qM ⊂ qN+M in the associative superalgebra U(qN+M ) . We construct a sequence of surjective homomorphisms U(qN ) ← A 1 N ← A 2 N ← . . . . We describe the inverse limit of the sequence of centralizer algebras A1N ,A 2 N , . . . in terms ...

The big from small construction was introduced by Kustin and Miller can be used to construct resolutions of tightly double linked Gorenstein ideals. In this paper, we expand on the DG-algebra techniques for building matrix factorizations a structure length $4$ construction. employed involve morphism Tate-like complex an acyclic exhibiting Poincar\'e duality. This induces homomorphisms which, af...

Abstract We study automatic injectivity of surjective algebra homomorphisms from $\mathscr{B}(X)$, the (bounded, linear) operators on X, to $\mathscr{B}(Y)$, where X is one following long sequence spaces: c0(λ), $\ell_{\infty}^c(\lambda)$, and $\ell_p(\lambda)$ ($1 \leqslant p \lt \infty$) Y arbitrary. En route proof that these spaces do indeed enjoy such a property, we classify two-sided ideal...

−→ (Ak, φk) and the operator algebras A = lim −→ (Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE = Homu(E⊗K, E⊗K) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is refer...

The functor taking global elements of Boolean algebras in the topos ShB of sheaves on a complete Boolean algebra B is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in B-valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial...

Let K be any unital commutative Q-algebra and z = (z1, · · · , zn) commutative or noncommutative free variables. Let t be a formal parameter which commutes with z and elements of K. We denote uniformly by K〈〈z〉〉 and K[[t]]〈〈z〉〉 the formal power series algebras of z over K and K[[t]], respectively. For any α ≥ 1, let D〈〈z〉〉 be the unital algebra generated by the differential operators of K〈〈z〉〉 ...