With some Calvinist classmates we sat in the first days as slightly uneasy newcomers on the benches of the Roman Catholic school, but soon became friendly the "long-established" Andor Kertész, then a 13-year-old. We already knew him by name: he was a son of the local Reformed Church Cantor and had an excellent reputation. "We want you to be also a good student like Bandi Kertész", I was told by my parents when they sent me to the gymnasium. His talent was known throughout the city. For us he was, like for many of his later friends and colleagues, "Bandi" Kertész. He organized us immediately into the so-called "small college" that is, into the group of younger schoolboys of the Reformed Student Union.

... once a week we came together for two or three hours and he entertained us with games appropriate for our age, with folk songs of various countries and he told us Bible stories with explanation. We proudly wore the mantle of service, the eight-pointed white "Calvin star", the badge of our union. On the vast courtyard of the Reformed Protestant culture house we played the inevitable football and other ball games that we had learned from Bandi. Here I introduced myself to ... Bandi's Bible competitions. Bandi would quote a Bible verse from the New Testament, and whoever was the fastest in finding the place in his own Bible got a point. Weekly he distributed four to five points and the competition - I even won twice - extended over an entire school year.

On completing this book I think with gratitude of my beloved teacher and friend, Professor Tibor Szele. His fruitful mathematical activity and his selfless and humanistic attitude touched me deeply. It was our plan to write a book on Artinian rings together, but his premature death prevented us from doing this.

When I was a student in the first year, I went boldly to Bandi's first scientific presentation in Szeged and he rejoiced when he saw me in the back row of the auditorium.

In Moscow I met Bandi, when he gave a lecture in the famous Algebra Seminar of Kurosh. It was a great honour for me that Kurosh invited even me to eat at his home in the evening where Kertész was also invited and, because he was just ending a visit to Moscow, also the Kiev group theorist Lev Arkad'evich Kaluznin. ... We were greeted by our hosts the Kuroshs and Mrs Kurosh served us their delicious food and equally delicious wines.

Rather than being a comprehensive account of the theory of Artinian rings, this book is an extremely well-written introduction to the theory of rings, with some applications to Artinian rings. From the pedagogical point of view, what is attractive about this book, besides its clarity, is the large number of exercises following each chapter and the careful development of the more important examples of rings. The development of the theory requires no previous knowledge of rings and it proceeds in the standard way via irreducible modules, the Jacobson radical, and the density theorem for primitive rings. Then the results are sharpened for Artinian rings. Besides the classical Wedderburn theorems, there are discussions of complete reducibility of representations, semi-simplicity of group rings, and projective and injective modules. The treatment of some of the above topics is quite novel.

This book deals with the classical structure theory of associative rings, with special emphasis on Artinian rings. ... The book is self-contained. The presentation is very clear and at the end of each chapter many well-chosen exercises are given.

An interesting and carefully written book, intended for students but containing some results not known to all professional mathematicians, illustrating the use of transfinite methods (chiefly Zorn's Lemma) in algebra.

This monograph is based on a lecture given in 1971 in Halle on the 125th anniversary of Cantor's birth, three years before the author's untimely death at the age of forty-five. The emphasis is on Cantor's set theory, but there is also a very sympathetic survey of his personality and his personal and academic life. There are much more extensive treatments elsewhere ... However, this book is distinguished by some interesting illustrations and, more importantly, by the warmth of the author's appreciation of his subject.

Should the reader notice that behind the lines there are confessions of a mathematician who among the different aspects of mathematics highlights especially the humanistic and aesthetic ones, then I will be richly rewarded for my efforts.

For me, however, he remained and still remains as a guiding star whose love and excitement about algebra brought and continues to bring light and encouragement to my research work ... At the time when I met him, I felt as if Professor Kertész were an angel sent by God to teach me mathematics. ... I still remember his excitement while talking at length about his joint work with Alfred Widiger describing the structure of Artinian rings for which the Jacobson radical is Artinian as a ring (cf. A Kertész and A Widiger, Artinsche Ringe mit artinschem Radikal, J. Reine angew. Math. 242 (1970), 8-15. After thinking about it for a while I felt that, in the light of the Wedderburn-Artin Theorem, this nice structure theorem could be obtained from a general and natural decomposition of Artinian rings. ... Inspiration stroke me and I finally obtained the desired theorem in 1976 ... Indeed, I could not have thought of creating this theorem without those inspiring conversations while I was under his tutelage. I believe he would have been delighted to learn about my theorem that includes the main theorem from Kertész and Widiger (1970) as a special case. ... In my research career, I often imagine him smiling at me and sharing his delight on my success.