We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed.

ACT does not suggest any regulations for columns under torsion. However, by all means, the number of such columns used in steel and concrete structures is abundant. In this paper, using the results of laboratory tests on 35 square and rectangular columns with intermediate slender ratios, relations for determination of torsional strengths of reinforced concrete under axial compression have been ...

A monoid M is a Cale monoid with base Q if for every nonunit x ∈ M there exists a positive integer n such that xn factors uniquely up to order and associates as elements from Q ⊆ M\M. An integral domain D is a Cale domain with base Q, if its multiplicative monoid of nonzero elements is a Cale monoid with base Q. We explore the basic properties of Cale monoids and integral domains. In particular...

An approximate numerical mthod is presented for analysis and determination of modal characteristics in straight, pretwisted non-unifom helicopter blades. The analysis considers the coupled flapwise bending (out of plane), chordwise bending (in plane), and torsion vibration of both rotating and non-rotating blades. The proposed method is based on the integral expansion of Green functions (struct...

In this article, we formalize a torsion Z-module and a torsionfree Z-module. Especially, we prove formally that finitely generated torsion-free Z-modules are finite rank free. We also formalize properties related to rank of finite rank free Z-modules. The notion of Z-module is necessary for solving lattice problems, LLL (Lenstra, Lenstra, and Lovász) base reduction algorithm [20], cryptographic...

We show that the Lie’s Theorem holds for Lie color algebras with a torsion-free abelian group G. We give an example to show that the torsion-free condition is necessary.

There is a great deal of literature on periodic rings, respectively, torsion-free rings (especially of rank two). The aim of this paper is to provide a link between these two topics. All groups considered here are Abelian, with addition as the group operation. By order of an element we always mean the additive order of this element. All rings are associative but not necessarily with identity. T...

Let R be a commutative ring with identity and let M be a torsion free R-module. Several characterizations of distributive modules are investigated. Indeed, among other equivalent conditions, we prove that M is distributive if and only if any primal submodule of M is irreducible, and, if and only if each submodule of M can be represented as an intersection of irreducible isolated components. MSC...

Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...