0-simple semigroups
John M Howie · 1995
Abstract The chapter begins with some elementary results on simple and 0-simple semigroups. A decomposition theorem for semigroups in general then indicates why an understanding of simple and 0-simple semigroups is important. The main result of the chapter is due to Rees (1940), and applies to 0-simple semigroups containing primitive idempotents. The Rees Theorem, strongly motivated by the Wedderburn-Artin Theorem for rings (see, for example, Cohn (1989)) has played a dominant role in the development of the subject.