Given an n×n matrix c over a unitary ring R, the centralizer of in full Mn(R) is called principal ring, denoted by Sn(c,R). We investigate its structure and prove: (1) If invertible with c-free point, or if R has no zero-divisors Jordan-similar all eigenvalues center then separable Frobenius extension Sn(c,R) sense Kasch. (2) integral domain matrix, cellular R-algebra Graham Lehrer. In particul...

The study of essential and strongly essential variables in functions defined on finite sets is a part of k-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal Algebra. On the basis of the concept of a separable set of variables in a term we introduce a new notion of complexity of terms, algebras and varieties and give e...

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and δ a generalized derivations of R. If [[δ(x), x], δ(x)] = 0 for all x ∈ R then either R is commutative or δ(x) = ax for all x ∈ R and some a ∈ C. We also obtain some related result in case R is a Banach algebra and δ is either continuous or spectrally

A generalization of the Reversed Compound Agent Theorem of Markovian process algebra is derived that yields separable, but non-product-form solutions for collections of interacting processes such as arise in multi-class queueing networks with Processor Sharing servers. It is based on an analysis of the minimal cycles in the state space of a multi-agent cooperation, which can be simply identifie...

In this paper we extend a result of Šemrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms ...

A remarkable result of Moln\'ar [Proc. Amer. Math. Soc., 126 (1998), 853-861] states that automorphisms the algebra operators acting on a separable Hilbert space is stable under "small" perturbations. More precisely, if $\phi,\psi$ are endomorphisms $\mathcal{B}(\mathcal{H})$ such $\|\phi(A)-\psi(A)\|<\|A\|$ and $\psi$ surjective then so $\phi$. The aim this paper to extend larger class Banach ...

Fräıssé studied countable structures S through analysis of the age of S, i.e., the set of all finitely generated substructures of S. We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fräıssé limit. We also show that degree spectr...

Say that a separable, unital C *-algebra D ≇ C is strongly self-absorbing if there exists an isomorphism ϕ : D → D ⊗ D such that ϕ and id D ⊗ 1 D are approximately unitarily equivalent *-homomorphisms. We study this class of algebras, which includes the Cuntz algebras O 2 , O∞, the UHF algebras of infinite type, the Jiang–Su algebra Z and tensor products of O∞ with UHF algebras of infinite type...