UTM’s beloved professor of mathematics, Ion JARDAN, who, for years, has been guiding students of the Technical University of Moldova, but also tutoring high school students aiming to successfully pass the BAC exams, has recently impressed the scientific community – by effectively defending his doctoral thesis in mathematical sciences at the Institute of Mathematics and Informatics “Vladimir Andrunachievici”.
Under the aegis of his scientific leader, Dr. Alexei CAȘU, Mr Jardan approached a very current topic in the field of Mathematical Logic, Algebra and Number Theory: “About special constructions in radical theory in module categories”. Although the foundations of research in the vast field of radical theory in modules was laid in the last century, in various dissertations, papers and monographs, written by his scientific coordinator also, the author aims to introduce and study new operations in the preradical class of a category of modules. In this context, he used the classical methods of algebra oriented towards the research of algebraic operations and their properties, combining them with a modern approach, related to the aspect and categorical language. Thus, four other new operations were added to the four known operations in the preradical class, namely: the left quotient relative to the union, the left co-quotient relative to the intersection, the left quotient relative to the intersection, and the left co-quotient relative to the union. At the same time, he determined the properties of these operations; investigated some particular cases of the new operations; established the relationships between them and some constructions in radical theory and described their behavior in the case of special type preradicals.
The main matter solved lies in the introduction and research of four new operations in the preradical class of a module category, which led to the enrichment of the instrumental work reserve in this class, for completing the study in the field of ring and module theory.
The research results were highly appreciated both by the official reviewers – prof., Dr. in Physics and Mathematical Sciences Dumitru BOTNARU, associate professor, Dr. Valeriu POPA, as well as the members of the specialized scientific council – acad., Dr. Vladimir ARNAUTOV (president of the Council), associate professor, Dr. Vladimir IZBAȘ (scientific secretary of CSȘ), acad., Dr. Mitrofan CIOBANU, Dr. Vasile URSU and associate professor, Dr. Elena COJUHARI, who emphasized the importance of this work in the development of radical theory in modules and its contribution to expanding the spectrum of knowledge in the field by introducing new operations in the pre-radical class and reformulating known things in order to use them for new particular cases.
Sincere congratulations, prof. Ion JARDAN, for the successful defence of the Doctoral Thesis in Mathematical Sciences!