In this study a systematic literature review was carried out to analyze the characteristics, indicators, limitations, benefits, and conclusions of scientific productions on industrial sustainability to propose a set of generic sustainability indicators for industrial organizations. The identification of the scientific productions occurred through the use of key words, in addition, the snowballing technique was also used, which resulted in a final set of 24 papers from 1998 to 2018. The technique used to select the indicators was the text mining with the help of NVivo Software. Finally, the multiple advisor method was applied. The main results show that the studies on sets of indicators with a Triple Bottom Line approach began in 1998. In addition, the papers show studies that analyze the industries generally being published by journals with a high impact factor, with authors from universities in Europe, from America and Asia, which use an average set of 30 indicators, with the lowest percentage of studies using mixed and mixed-scale approaches. The limitations revealed by the papers are the lack of initiative and actions of organizations for the adoption of sustainability. The benefits are linked to the informational assistance they provide to managers in decision-making, and the conclusions reveal a lack of research on the use of the praxis of the set of sustainability indicators in industrial organizations. In this sense, we conclude that the set of indicators suggested in this study is in line with the theoretical findings of the reviewed literature, with a balance between the Triple Bottom Line aspects and the synthetic number of indicators that provide the ease of its application and analysis.

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In this paper we study higher derivations of prime and semiprime rings satisfying linear relations. We extend several results which are known for algebraic derivations and we prove some other results.

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Let R be a ring, and α be an endomorphism of R. An additive mapping H: R → R is called a left α-centralizer (resp. Jordan left α-centralizer) if H(xy) = H(x)α(y) for all x, y ∈ R (resp. H(x 2) = H(x)α(x) for all x ∈ R). The purpose of this paper is to prove two results concerning Jordan α-centralizers and one result related to generalized Jordan (α, β)-derivations. The result which we refer state as follows: Let R be a 2-torsion-free semiprime ring, and α be an automorphism of R. If H: R → R is an additive mapping such that H(x 2) = H(x)α(x) for every x ∈ R or H(xyx) = H(x)α(yx) for all x, y ∈ R, then H is a left α-centralizer on R. Secondly, this result is used to prove that every generalized Jordan (α, β)-derivation on a 2-torsion-free semiprime ring is a generalized (α, β)-derivation. Finally, some examples are given to demonstrate that the restrictions imposed on the hypothesis of the various theorems were not superfluous.