Growth of Rees Quotients of Free inverse Semigroups Defined by Small numbers of Relators

Growth of Finitely Presented Rees Quotients of Free Inverse Semigroups

We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial growth if and only if it has bounded height. This occurs if and only if the set of nonzero reduced words has bounded Shirshov height and all nonzero reduced but not cyclically reduced words are nilpotent. This occurs also if and only if the set of nonzero geodesic words have bounded Shirshov height. We a...

The Uniform Word Problem for Groups and Finite Rees Quotients of E-unitary Inverse Semigroups

The Loop Problem for Rees Matrix Semigroups

We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem is context-free. We also establish some results concerning loop problems for subsemigroups and Rees quotients.

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...

Function spaces of Rees matrix semigroups

We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.