**Ottó Steinfeld**was born into a Jewish family in Szarvas, a town Békés county in south eastern Hungary. He grew up in the town where he attended school showing what a talented young man he was. He was 15 years old when World War II began but, since Hungary was allied to Germany, there was no invasion of the country. Steinfeld was able to continued his schooling. He was not allowed, however, to continue his studies at university despite his achievement since this was prevented by anti-Jewish laws. He could only obtain a job involving manual labour and he became an apprentice mason. He qualified as a mason before the German army invaded Hungary in March 1944. Before this event the Hungarian government had discriminated severely against its Jewish citizens, both economically and politically, but they had largely been spared the concentration camps of the Nazis. After the German invasion, however, Dome Sztojay, a Nazi supporter, was installed as Hungarian prime minister and Hungarian Jews began to be deported to the gas chambers in concentration camps in Poland.

Steinfeld was called up for military service in 1944 but as a Jew he was considered an "unreliable person" and forced to work as a manual labourer in deplorable conditions. He spent a year working in desperate conditions during which time his health deteriorated markedly - he had severe problems with his kidneys and lungs. As a consequence he had health problems for the rest of his life. During this time he learnt that his parents had died in a concentration camp where they had been taken under the new policy of Dome Sztojay.

Soviet troops entered Hungary in September 1944 and until April 1945 the country became a battlefield, sacked both by retreating German troops and by advancing Soviet troops. After the war ended Steinfeld was able to attend university. He entered Szeged University in 1945 where he studied mathematics and physics. He was particularly attracted to algebra by the lectures of László Rédei. After graduating with his diploma in 1950, he was offered a post as an assistant at Szeged University. He taught at Szeged while working for his Candidate's degree under the guidance of Rédei. During this period Rédei was working on ideas that he published in *Die Holomorphentheorie für Gruppen und Ringe* Ⓣ (1954). Basically he was seeking appropriate analogues in ring theory for certain concepts used in the theory of groups and he did this by looking at the corresponding notions in semigroups. It is interesting that most of Steinfeld's research went in the other direction for he often took ideal theoretic properties of rings and looked for analogues in semigroup theory, semiring theory, or the theory of partially ordered algebraic structures.

In 1955 Steinfeld was awarded his Candidate's degree, and the following year he left Szeged to take up an appointment in the Mathematical Institute of the Hungarian Academy of Sciences in Budapest. He was awarded a D.Sc. in 1969 and, two years later, became Head of the Department of Algebra of the Hungarian Academy of Sciences. He held this position until 1982 when, at the age of 58, he was forced to retire due to ill health.

In [1] Márki lists 65 publications by Steinfeld. His early publications, while he was working for his Candidate's degree, were *Bemerkung zu einer Arbeit von L Kalmár* Ⓣ (1951), (with L Rédei) *Über Ringe mit gemeinsamer multiplikativer Halbgruppe* Ⓣ (1952),*Über die Nullteilerfreiheit von Ringen* Ⓣ (1942), *Remark on a paper of N H McCoy* (1953), and *On ideal-quotients and prime ideals* (1953). In this last mentioned paper Steinfeld introduced the concept of a quasi-ideal. This was a concept which he continued to develop throughout his career. The paper also considers applications of ideal theory in rings to Schreier extension theory in groups in the same spirit as Rédei's paper *Holomorphentheorie für Gruppen und Ringe* Ⓣ (1954) which we mentioned above. Much of Steinfeld's contributions to quasi-ideals is contained in his monograph *Quasi-ideals in rings and semigroups* (1978). H J Weinert, in a review of the book, notes that Steinfeld introduced the notion of a quasi-ideal in *On ideal-quotients and prime ideals* (1953) and since then:-

Other topics on which Steinfeld undertook research included the structure of simple artinian rings, for example in... results on those quasi-ideals have been published in more than fifty papers, showing the fruitfulness of this notion, particularly in revealing similarities and differences between rings and semigroups. The main part(about100pages)of this excellent book gives a systematic and self-contained survey on this subject.

*Some characterizations of semisimple rings with minimum condition on principal left ideals*, and analogues in other algebraic systems. His article

*Über die Verallgemeinerungen und Analoga der Wedderburn-Artinschen und Noetherschen Struktursätze*Ⓣ (1967) discussed generalizations of the Noether and Wedderburn-Artin characterizations of the semi-simple and simple Artinian rings to

*F*-rings, to the

*MHL*-rings, for semi-simple linear compact rings, for semirings, for semi-simple near-rings, and for semi-groups which are unions of completely 0-simple. In the paper (with L Rédei)

*Einiges über Gruppoid-Verbände mit Anwendungen auf Gruppen, Ringe, Halbgruppen*Ⓣ (1974) the authors generalise concepts from groups, rings, and semigroups to groupoid lattices. Steinfeld was also much interested in primness, including prime ideals and prime elements in partially ordered semigroups. An example of a paper on this topics is (With L Fuchs)

*Principal components and prime factorization in partially ordered semigroups*(1963). J A H Shepperd writes:-

Márki, in [1], describes Steinfeld's character:-Two new sets of conditions are obtained for unique prime factorisation in a partially ordered semigroup(not necessarily commutative), generalising the fundamental theorem or commutative ideal theory. The concept of principal component is introduced and its properties are studied.

Ottó Steinfeld was a man with high moral standards. When important matters were at stake, he always tried to disregard not only his personal interests but even his social attachments. He was full of good intentions, always ready to help and protest against injustice, even in times and cases when such actions meant a danger to himself. Anyone who really got to know him could not help loving him.

**Article by:** *J J O'Connor* and *E F Robertson*