We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a c...

We provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra. c © 2006 Elsevier Ltd. All rights reserved.

Let A be a separable unital C-algebra. It is shown that A is type I if and only if the CNT-entropy of every inner automorphism of A is zero.

In this paper we gemeralize the primitive element theorem to the generation of separable algebras over fields and rings. We prove that any finitely generated separable algebra over an infinite field is generated by two elements and if the algebra is commutative it can be generated by one element. We then derive similar results for finitely generated separable algebras over semilocal rings. A) P...

We prove a necessary and sufficient condition for the states which satisfy strong subadditivity of von Neumann entropy with equality on CAR algebra and we show an example when the equality holds but the state is not separable.

In this paper we investigate a ring of delay-differential operators, which appears in the study of time-delay systems with commensurate point-delays. Besides point-delay differential operators, this ring contains also certain distributed delays. It can be described as a certain algebraic extension of the ring of point-delay differential operators as well as a convolution algebra of compact supp...

Let (K,v) be a valued field, and μ an inductive valuation on K[x] extending v. Gμ the graded algebra of over K[x], κ maximal subfield subring formed by homogeneous elements degree zero. In this paper, we find algorithm to compute field residual polynomial operator Rμ:K[x]→κ[y], where y is another indeterminate, without any need perform computations in algebra. This leads OM factorization separa...