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A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.
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Ascending sequences of idempotents in inverse semigroups
I've enocuntered the following question in my current research, and I'd appreciate any help you could give me. This is probably well known to experts on the subject.
Let $S = \langle K \rangle$ be a …
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Quasi-isometries and E-unitary inverse semigroups
Let $S = \langle K\rangle$ be a finitely generated inverse semigroup, where $K \subset S$ is a fixed, finite and symmetric set of generators.
Preliminaries: Recall that we say that $s, t \in S$ are $ …