Take the 2-minute tour ×  Is there any concept in monoids that
is similar to the concept "conjugate class" in groups? For
example, are there any such similar concept in symmetric inverse
monoids? Thank you very much.  share|improve this question  3
Answers 3  up vote 8 down vote accepted  There are several
different definitions of conjugacy for semigroups. For inverse
semigroups the best, in my opinion, definition is this: $a$ is
conjugate to $b$ if there exists $t$ such that $t^{-1}at=b$,
$tt^{-1}=e, t^{-1}t=f$, $ae=ea=a$, $bf=fb=b$. In this case the
conjugacy relation is an equivalence relation and the concept of
conjugacy classes is well defined, and easy to describe in the
case of symmetric inverse monoids. See, for example, the
following article by Akihiro Yamamura, http://journals.cambridge
.org/download.php?file=%2FJAZ%2FJAZ70_02%2FS1446788700002639a.pd
f&code=213e793755d6e9249ea5704c1f57a0b3 .  share|improve this
answer @Mark, thank you very much. –  Jianrong Li Jan 15 '11 at
3:25 Mark, are Green's (sem