The present paper is a note on the relative tensor degree of finite groups. This notion generalizes the tensor degree, introduced recently in literature, and allows us to adapt the concept of relative commutativity degree through the notion of nonabelian tensor square. We show two inequalities, which correlate the relative tensor degree with the relative commutativity degree of finite groups. 1...

We present direct arguments for non-commutativity of spheres in the AdS/CFT correspondence. The discussion is based on results for the SN orbifold SCFT. Concentrating on three point correlations (at finite N) we exhibit a comparison with correlations on a non-commutative sphere. In this manner an essential signature of non-commutativity is identified giving further support for the original prop...

In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asymptotic commutativity property, generalizing the notion of relative locality proved by Borch...

In this paper, we try to focus the reader's interest on the problems that transactional systems have to resolve for taking advantage of commutativity in a serializable and recoverable way. Our framework is, (as others), based on the use of conditional commutativity on abstract date types. We present new features that have not been found in the literature hitherto, that both increase concurrency...

We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on c...

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is ...

Rewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of non-termination inherent to the use of identities. We build up on this idea in two ways: by giving a complete set of rules for completion modulo these axioms; by showing how to build appr...