Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...

We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the Auslander Conjecture. Along the way, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups of π1 to have vanishing...

The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...

For a finite dimensional algebra A over an algebraically closed field, let T (A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if TA is a tilting module and B = EndTA, then T (A) is tame if and only if T (B) is tame. Introduction. Let k be an algebraically closed field. In this paper, an algebra A is always assumed to be associative, with an ide...

We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only it is seemingly injective in following sense: there factorization of identity M $$I{d_M} = vu:M\buildrel u \over \longrightarrow B(H)\buildrel v M$$ with normal, unital, completely contractive. As corollary, separable predual, isomorphic (as Banach space) to B(ℓ2). For instance this applies (rather...

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable ...

The simple entanglement of N -body N -particle pure states is extended to the more general M -body or M -body N -particle states where N 6= M . Some new features of the M -body N -particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.

Proof. The intersection P of all subfields of F is a field by Exercise 1.4. Consider the ring homomorphism φ : Z → F given by φ(n) = n · 1. Since any subfield contains 1 and is closed under addition, imφ is contained in P . If Char F = p 6= 0 then imφ is isomorphic to Z/pZ = Fp. Since this is a field, we have P = imφ ∼= Fp. If Char F = 0 then φ is injective. Define φ̂ : Q → F by φ̂(m/n) = φ(m)/φ(...

A finite simple graph ? determines a quotient P? of the pure braid group, called graphic arrangement group. We analyze homomorphisms these groups defined by deletion sets vertices, using methods developed in prior joint work with R. Randell. show that, for K4-free ?, product maps is injective, embedding free groups. Then residually free, torsion-free, torsion-free nilpotent, and acts properly o...

In this paper, we prove that for a generic choice of tame (or compatible) almost complex structures J on a symplectic manifold (M, ω) with its first Chern class c1(M, ω) = 0 for n ≥ 3, all somewhere injective J-holomorphic maps from any closed Riemann surface into M are embedded.