Márki László, Wiegandt Richárd: Theory of Radicals

Radicals have arisen from structural investigations in rings, but later on they infiltrated into various branches of algebra as well as into topology and relational structures. The first conference devoted solely to radical theory took place in Eger, Hungary, in 1982. Following the success of the Eger conference, similar meetings were organised every three years: in 1985 in Krems, Austria, in 1988 in Sendai, Japan, and in 1991 in Szekszård, Hungary. Let us mention also the two conferences entitled Rings, Modules and Radicals, the first of which took place as early as 1971 in Keszthely, Hungary, and the second in 1987 in Hobart, Australia.
The Szekszård meeting also turned out to be an important event in the field of radical theory. It became visible that the most substantial progress of the foregoing three years was made in radicals of semigroup rings and graded rings as well as in radicals of near-rings. For most of the participants, a new aspect of the theory became manifest in R. Göbel's survey on radicals of abelian groups, where logical considerations play an eminent part.