Proceedings of the Edinburgh Mathematical Society: Volume 28 -

Semigroups of high rank II doubly noble semigroups
Emilia Giraldes
Published online by Cambridge University Press:

20 January 2009, pp. 409-417
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This paper is a sequel to [2]. By a semigroup of high rank we mean a semigroup such that for s1≠s2, 〈S\{s1,s2}〉⊂S (properly). Semigroups of high rank such that 〈S\{s}〉⊂S(royal semigroups) were classified in [2], where it was also shown that for a noble semigroup (i.e. a semigroup of high rank such that there exists a superfluous element z in S for which 〈S\{z}〉S) there exists eithere exactly one superfluous element or exactly two superfluous elements [2, Theorem 3.7].

Proceedings of the Edinburgh Mathematical Society