Amalgamated free products of von Neumann algebras were first used by S. Popa ([26]) to construct an irreducible inclusion of (non-AFD) type II1 factors with an arbitrary (admissible) Jones index. Further investigation in this direction was made by K. Dykema ([10]) and F. Rădulescu ([27, 29]) based on Voiculescu’s powerful machine ([40, 41, 44]), and F. Boca ([4]) discussed the Haagerup approxim...

We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-c...

Homomorphic encryption (HE) is an scheme that provides arithmetic operations on the encrypted data without doing decryption. For Ring-based HE, uses a polynomial ring as building blocks, performance improvement of unit HE has been achieved by two kinds efforts. The first one through accelerating operations. However, it does not facilitate optimizations across such fusing second implementing hig...

An embedding question for full (i.e. universal) amalgamated free products of C∗–algebras is raised, and solved in part. This is used to give a necessary and sufficient condition for the full amalgamated free product of finite dimensional C∗–algebras to be residually finite dimensional.

We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...

Let R be a commutative ring with identity and let I be an ideal of R. Let R 1 I be the subring of R×R consisting of the elements (r,r + i) for r ∈ R and i ∈ I. We study the diameter and girth of the zero-divisor graph of the ring R 1 I.

Subrahmanian 14] uses annotated logic 2] to integrate a set of deductive databases in an unique amalgamated database called amalgam. The amalgam, in addition to the disjoint union of the databases, contains a supervisory database. The supervisory database is a set of clauses (called amalgamated clauses) which resolve connicts due to inconsistent facts and compose uncertain information of diiere...

Let R be a discrete valuation ring with fraction eld K and X a at R-scheme. Given a faithful action of a K-group scheme GK over the generic bre XK , we study models G of GK acting on X. In various situations, we prove that if such a model G exists, then there exists another model G′ that acts faithfully on X. This model is the schematic closure of G inside the fppf sheaf AutR(X) ; the major di ...