Inverse Semigroups of Left I-quotients
نویسنده
چکیده
We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semigroups (a step that has previously proved to be awkward). We also put some earlier work on Gantos into a wider and clearer context, and pave the way for further progress.
منابع مشابه
Left I-quotients of band of right cancellative monoids
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...
متن کاملNo : 11 Title : ‘ Primitive Inverse Semigroups of Left I - Quotients ’ Author ( S ) :
A subsemigroup S of an inverse semigroup Q is a left I-order in Q, if every element in Q can be written as a−1b where a, b ∈ S and a−1 is the inverse of a in the sense of inverse semigroup theory. We study a characterisation of semigroups which have a primitive inverse semigroup of left I-quotients.
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