On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

The main benefits associated with health and safety management systems certification in Portuguese small and medium enterprises post quality management system certification

The purpose of this study is to characterize how Portuguese Small and Medium Enterprises (SMEs) view the Occupational Health and Safety Management Systems (OHSMSs) certification process, after receiving the Quality Management System (QMS) certification. References were based on the ISO 9001 standard for a QMS and OHSAS 18001 for OHSMS. The method used to evaluate the implemented systems, was by form of questionnaire. Those questioned had to have a certified quality management system, an implemented OHSMS and be a SME. The questionnaire was sent to 300 SMEs; 46 responses were received and validated. Of them, only 12 SMEs had the OHSMS certificate according to OHSAS 18001. Within those 12 companies that participated: 7 SMEs are from the industrial sector; 3 belong to the electricity/telecommunications sector and 2 SMEs are from the trade/services activity sector. The size of the sample was small, but corresponds to Portuguese reality. Moreover, 34 SMEs did not have the OHSMS certificate. The questionnaire requested the main reasons for SMEs to opt for non-certification and it was related with high costs, while the main reasons to certificate were, among others, needed to eliminate or minimize risks to workers. The main benefits that Portuguese SMEs have gained from the referred certifications have been, improved working conditions, ensuring compliance with legislation and better internal communication about risks and hazards. Also presented are the main difficulties in achieving an OHSMS certification including high certification costs, difficulties motivating personnel, difficulties in changing the company’s culture and increased bureaucracy.