An associative or alternative algebra A is Noetherian if it satisfies the ascending chain condition on left ideals. Sinclair and Tullo [21] showed that a complex Noetherian Banach associative algebra is finite dimensional. This result was extended by Benslimane and Boudi [5] to the alternative case.For a Jordan algebra J or a Jordan pair V, the suitable Noetherian condition is the ascending chain condition on inner ideals. In a recent work Benslimane and Boudi [6] proved that a complex Noetherian Banach Jordan algebra is finite dimensional.Here we show the following results:(i) the Jacobson radical of a Noetherian Banach Jordan pair is finite dimensional;(ii) nondegenerate Noetherian Banach Jordan pairs have finite capacity;(iii) complex Noetherian Banach Jordan pairs are finite dimensional.

The main objective of this research paper consists in introducing the concept of [Formula: see text]-derivations acting on Banach–Jordan pairs and Banach–Jordan algebras and giving an automatic continuity result of the operators in question under some algebraic conditions. Concretely, we prove that [Formula: see text]-derivations defined from a Banach–Jordan pair [Formula: see text] into a strongly prime Banach–Jordan pair [Formula: see text] are automatically continuous under the assumptions that the socle [Formula: see text] is nonzero and [Formula: see text] is an isomorphism from [Formula: see text] into [Formula: see text]. Similar results for Banach–Jordan algebras hold to be true.

The issue of teacher training for the three school cycles was raised in this research. This is part of a diagnostic perspective of discomfort likely to affect the training curriculum in place at regional centers of education and training (CRMEF) in Morocco. Such discomfort would inevitably have negative repercussions on the performance of teacher training or even the education system as a whole. We are committed to making suggestions regarding potential remedies. The theoretical part of this research focused on the professionalization of the teacher's profession in its close relationship with a foundation of professional skills to be developed among future teachers. We have cited definitions developed by certain authors (Bourdoncle, 1991), (Lang, 1999), (Maubant and Roger, 2012), (Wittorski, 2008) which illustrate the concept of professionalism in the field of education. The practical part involved the strategy of answering the fundamental questions inherent in the training of future teachers, in search of possible solutions. Our research is indeed motivated by our keen desire to contribute to the development of a new training curriculum. But to do this, it is imperative to: • Return to the experiences, innovations and approaches formerly adopted by the Moroccan education system, in particular after the advent of the national charter for education and training. • Capitalize on previous national experiences relating to training, keep its benefits and adapt it to innovations in terms of professionalism. • Open up to benchmark experiences and modern international educational orientations. • Work according to a new regime which aims to promote the teaching practice so that pedagogical action is exclusively centered on the learner. This research is also part of our commitment to carry out our sincere intention, that of making our contribution, humble as it is, to promote the quality of training of future teachers, which is the sine qua non of professionalizing and making profit. learning in our schools. Indeed, it is the good intentions combined with the actions that are likely to generate the expected results.

This research is part of a perspective of highlighting the impact of education and training on the qualification and promotion of professional human resources skills. It also helps to highlight the dialectical and substantial correlation between the expansion of human capital and the economic, social and cultural development of different nations. Moreover, it is commonly accepted among the various political or economic actors that education and training is of major importance in the progress made by nations in the various sectors and even an essential vector of their rebirth. It shows that the governments of various countries are sparing no effort in investing heavily in this education sector. They do not care at all about the colossal budgets that this requires, and the immediate repercussions that they should imperatively generate on the economic and social aspects, as long as they are convinced that the good performance of the education system inevitably has repercussions in the short term, in the medium or long term in the various productive sectors, through the wealth they are likely to generate. This research is structured in two parts, one theoretical and another practical, as follows: the theoretical part emphasizes the key factors that intervene in the production of wealth and which consequently drive economic and social development, in this case, human capital and financial capital. The practical part is dedicated to a statistical study relating to the correlation between human capital and economic growth. The research is closed by certain suggestions inherent to the topic discussed in this article.

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