let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish a criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corre...

We give the nuclear analogue of Dadarlat’s characterization of exact quasidiagonal C∗-algebras. Specifically, we prove the following: Theorem 0.1. Let A be a unital separable simple C∗-algebra. Then the following conditions are equivalent: i) A is nuclear and quasidiagonal. ii) A has the stabilization principle. iii) If π : A → M(A ⊗ K) is a unital, purely large ∗-homomorphism, then the image π...

For any (unital) exchange ring R whose nitely generated projective modules satisfy the separative cancellation property (A A = A B = B B =) A = B), it is shown that all invertible square matrices over R can be diagonalized by elementary row and column operations. Consequently, the natural homomorphism GL 1 (R) ! K 1 (R) is surjective. In combination with a result of Huaxin Lin, it follows that ...

Let G be the group of projectivities stabilizing a unital U in PG(2, q2) and let A,B be two distinct points of U . In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q − 1 greater than 2(√q − 1), then U is an ovoidal Buekenhout–Metz unital. From this result two group theoretic characterizat...

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...