Steinfeld Ottó: Quasi-ideals in rings and semigroups - Disquisitiones mathematicae Hungaricae 10. (Budapest, 1978)
O. Steinfeld QUASI-IDEALS IN RINGS AND SEMIGROUPS In recent years, there has been growing interest in algebraic research dealing with analogous results on associative rings and semigroups. The notion of quasi-ideal, introduced by the author some 20 years ago, has proved especially useful in revealing the similarities and differences between these two classes of algebraic systems. The author has made a considerable contribution with his 10 papers on quasiideals of rings and semigroups to an area now being treated by about 20 mathematicians from different parts of the world. More than 50 papers have appeared on the subject, moreover quasi-ideals have found their way into a number of books, too. The book proper gives a systematic survey of the most important results on quasiideals in rings and semigroups, and calls attention to some unsolved problems. The main results deal with Green’s 35-relation, with the characterizations of Neumannregular rings and semigroups by means of quasi-ideals, and with structure theorems of Noether and Wedderbum-Artin type on semiprime rings and primitive regular semigroups. A decomposition theorem generalizing the structure theorems of Noether and Wedderbum-Artin type can also be found in the appendix. AKADÉMIAI KIADÓ Publishing House of the Hungarian Academy of Sciences BUDAPEST