Ž . A group G is LERF locally extended residually finite if for any finitely generated subgroup S of G and for any g f S there exists a finite index subgroup S of G which contains S but not g. Using graph-theoretical methods we give 0 algorithms for constructing finite index subgroups in amalgamated free products of groups with good separability properties. We prove that a free product of a fre...

To this end let X and Y be 3–manifolds with incompressible boundary homeomorphic to a connected surface F . It is not difficult to show that if HX and HY are Heegaard surfaces in X and Y then we can amalgamate these splittings to obtain a Heegaard surface in X∪F Y with genus equal to g(HX)+g(HY )−g(F) (see, for example, Schultens [14]). Letting g(X), g(Y), and g(X∪F Y) denote the minimal genus ...

In this paper, we study the transfer of notion $m$-clean ring (i.e., a in which every element is sum unit and an $m$-potent element) to amalgamated bi-amalgamated rings. We also find many sufficient necessary conditions for m-clean property Received: March 7, 2023Accepted: May 31, 2023

Journal of Algebra, Vol. 111, No. 1, Nov 1987, 133–153. Richard E. Borcherds, D.P.M.M.S., University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, England. The study of automorphism groups of unimodular Lorentzian lattices In,1 was started by Vinberg. These lattices have an infinite reflection group (if n ≥ 2) and Vinberg showed that the quotient of the automorphism group by the reflection gr...

Hardware lock-elision (HLE) introduces concurrency into legacy lockbased code by optimistically executing critical sections in a fast-path as hardware transactions. Its main limitation is that in case of repeated aborts, it reverts to a fallback-path that acquires a serial lock. This fallback-path lacks hardwaresoftware concurrency, because all fast-path hardware transactions abort and wait for...

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a structure theory for the weak operator topology closed algebras generated by these representations, which we call free semigroupoid algebras. We characterize semis...

We introduce a new general construction, denoted by R 1 E, called the amalgamated duplication of a ring R along an R–module E, that we assume to be an ideal in some overring of R. (Note that, when E = 0, R1E coincides with the Nagata’s idealization R⋉E.) After discussing the main properties of the amalgamated duplication R 1E in relation with pullback–type constructions, we restrict our investi...