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FINITE PRESENTATIONS OF SEMIGROUPS AND FREE
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0-simple apply assertion associated assume belong called cancellative cardinal centered clear clearly completely simple completes the proof conclude condition Consequently consider consists construction contains Conversely corollary corresponding deﬁned deﬁnition denote determined element embedded empty equation equivalence Exercise exists fact factor ﬁnite ﬁrst follows free semigroup further given gives Hence holds homomorphism idempotents identity element immediately implies inﬁnite inverse semigroup isomorphic Lemma Let H letter Malcev mapping Math means minimal normal notation O-minimal right ideal Observe obtained one-to-one operand operator p-class pair partial present primitive principal proper prove quotient rank regular relation replaced representation result reversible right congruence S-step satisﬁes sequence shown sides Similarly simple semigroup strong subgroup subsemigroup subset Suppose syllable Theorem transformations transitive union unique unitary whence zero