Abstract
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.
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