I cannot fail to recall with deep gratitude the memory of my parents. My mother succeeded in transplanting a fraction of the latent mathematical talent she inherited from her father. My father, a leading Finno-Ugric linguist, set an example (even in the absence of state recognition) of the sacrifice and selflessness of research and the importance of investigating fundamental scientific questions. His influence on my life is immeasurably greater than that of anyone else.

At the beginning of the 1941-42 school year, Paul Erdős's father visited the principal [Dávid Fokos-Fuchs] of the Jewish Gymnasium in order to secure a classroom. The Jewish Cultural Association had organised a special course for high school students interested in mathematics, and needed a place to meet once a week. The instructor was Tibor Gallai, a very talented mathematician and a superb teacher (without a job). The school principal agreed, under one condition: his son (me) would also be admitted to the course. [There were] 8 or 10 students in the group. Most of us were in high school. Some had already graduated, but because of the numerus clausus (quota against Jews) weren't allowed to enter the university.

Before and after class we had long discussions on the solutions of the take-home problems, possible generalisations, and so on. ... [There were only a] few in the course who would survive the Holocaust.

I was not accepted to the Budapest University of Technology because of the Jewish quota, but after six months of working in a factory I was allowed to enrol in the Faculty of Humanities as a teacher candidate majoring in mathematics and physics.

In 1945, immediately after the war, it was not possible to study much mathematics at the University of Budapest. Professor Fejér grew weak during the German occupation. Professor Kerékjártó could no longer hold lectures due to his illness. The wartime suffering caused by military service, the terrible prisoner of war situation and inhuman labour did not break us.

... the legendary meetings of the "Big Five" were different from ordinary seminar lectures, not only in that the members were constantly interjecting questions and ideas, but also in that they laughed and joked almost non-stop, where the subject of the joke was usually the topic being discussed or the way it was presented. "It was wonderful to learn some serious mathematics alongside all the jokes," said Páles, quoting Fuchs.

Let R be an integral domain with identity element. An ideal Q is defined to be quasi-primary if $ab \in Q$ implies that some power of a or of b is in Q; Q is quasi-primary if and only if its radical is prime. If R is Noetherian, then every ideal is the intersection of a finite set of quasi-primary ideals such that no proper subset has quasi-primary intersection. The numbers of quasi-primary components and their radicals are uniquely determined. The connection between this decomposition and those given by E Noether in 1921 is discussed.

Julius König and Michael Bauer had a number of papers in classical algebra (the former even had a frequently quoted book), and Joseph Kürschák was the founder of classical valuation theory, but they died before World War II and did not have any followers. Abstract algebra was non-existent in Hungary. As a result, no guidance was available for students interested in abstract algebra; we had to learn it from books and articles. Undoubtedly, we benefited tremendously from the congenial, research-oriented atmosphere and the support of many established mathematicians, though the "abstract nonsense" was frowned upon by several application-oriented colleagues.

... for work on the theory of structural algebra.

The classrooms were always full, students went there to enjoy the beauty and clarity of his lectures. With his regular algebra seminars he started building up an "algebra school" from nothing. He never pushed his students to follow his special interest in algebra, but he rather helped them to develop their own field according to their characteristic abilities. ... His main mission was to serve the best interest of the students and mathematics, and to help young mathematicians in getting involved in research. He did not show the slightest opportunism, even in time when it was a means of survival. This was one of the main reasons that his administrative career was held back and eventually broken.

Professor Fuchs has packed a very great amount of important and interesting group theory into it; he always explains what he intends to do, and why; he not only proves theorems but also discusses their significance.

The author has been eminently successful in giving a complete, detailed, and easily understandable account of the present status of the theory of abelian groups with special emphasis on results concerning structure problems.

The combination in one book of treatise and textbook is not a new phenomena in mathematical publishing. However, rarely has it been done with such felicity and success as in Fuchs' book.

I vividly remember the first talk by László Fuchs I attended as a student in Baer's seminar at Frankfurt University in 1964, which took place in the physics lecture hall, where László Fuchs explained consequences of the existence of basic subgroups of abelian groups. Although abelian group theory was not my major topic at that time, in contrast to other speakers, Fuchs left a permanent impression.

Of that year spent in New Orleans in the student Rosen House, where we had a small two-room flat as accommodation, and at Gibson Hall, a beautiful neo-Gothic building where Tulane University's mathematics department was located, Paola [Salce's wife] and I have the vivid memory of a happy time. ... László taught a course on Abelian groups to PhD students, whose notes I still keep, filling several notepads. In that course I learnt the main results on totally projective groups, which made me passionate about the theory of Abelian p-groups. I then became interested in and studied for many months the existing literature on this theory, hitherto almost completely unknown to me. One evening we were invited to dinner at László's house on Laudun Street, where we got to know Shula, who was pregnant with Terry. Paola and I certainly did not think on that occasion that we would become close friends with Shula and László, as in fact happened a few years later. Thanks to László's great willingness to help, we tackled together, with him leading and me following, some problems on Abelian groups, so that by the end of the year spent at Tulane I had three published papers with László as co-author.

Volumes I and II represent a truly masterful scholarly achievement, and will certainly be both the standard references and standard texts in the subject for years to come.

Professor László Fuchs is an outstanding researcher and author. His extraordinary productivity and influential monographs in the areas of abelian groups, ordered algebraic structures, rings, and modules, have directly impacted the growth and direction of research of these important areas of algebra.
...
László started his research career by diving deep into the ideal theory of rings, beginning with his thesis in commutative ideal theory. This was written without a thesis supervisor; indeed, he was the only algebraist in Budapest at the time. His work in this area remained a primary focus for the first decade of his career, and within seven years of submitting this thesis, he had earned the Kossuth Prize, the highest national award for scientists in Hungary, and he was promoted to full professor. All of this was largely based on his "first" career, that of a commutative ring theorist. Recently, after impressive and far-ranging detours into abelian groups, ordered algebraic systems and module theory, he has turned his attention back to the ideal theory of commutative rings, thus completing a full circle of his amazing journey through several important areas of research.

I was very happy when László asked me to collaborate with him on the first book on modules over valuation domains. But I was more proud and conscious of the task proposed to me to write our second book on modules over non-Noetherian domains. It soon seemed to be a really hard job, but the experience of László, our close friendship and his strong resolution removed my doubts. In both these experiences I admired the qualities of an outstanding mathematician and of a generous man. László has an extraordinary capacity for assimilating and elaborating large and complex portions of mathematics, for simplifying proofs and for finding new perspectives on old results. Other impressive qualities are his obstinacy in pursuing a result through a full immersion in the problem, and his capacity for identifying the good veins in the great mine of mathematics.

Interviewed in his trash-strewn front yard, Fuchs said he couldn't believe how in one day, this group of Jews did more to help him and his wife than anyone has done in the four months since Katrina shattered their lives. "I'm not really accustomed to asking for help, so it's very difficult to find words to express how we feel about complete strangers coming to help us," he said. Added Shula, "It's beyond words. It's overwhelming. This is our people. It makes us believe."

Looking back over his mathematical career, Fuchs explained how his path led him from primal ideals theory, through the theory of ordered algebraic structures, to the study of Abelian groups and unsolved problems.

"This has remained my favourite subject all my life; I have written three books on Abelian groups," he continued. "Perhaps I made a mistake by changing my research problems frequently, but I confess I couldn't resist trying to solve an interesting problem that arose. I was eighty years old when I retired, but there was no way I could stop doing mathematics. During the last twenty years I have written about many old problems and clarified many interesting questions in a new field for me, the new branch of commutative rings. I am happy to say that I have managed to prove an important existential theorem. The theorem: mathematics still exists after ninety years. This is not a new theorem, but we can agree that it is not easy to prove. It is a common practice to make promises of future work at the occasion of recognition. At my age, this makes no sense. But I can safely say that my award confirms my ambition to prove that mathematics still exists after a hundred years."

... in recognition of an outstanding life's work and also in memory of his service as Dean of the Faculty of Mathematics, Physics and Chemistry at Eötvös Loránd University between 1954 and 1956.