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MAXIMAL SUBGROUPS OF FREE IDEMPOTENT GENERATED SEMIGROUPS OVER THE FULL LINEAR MONOID
We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal
THE IDEMPOTENT-GENERATED SUBSEMIGROUP OF THE KAUFFMAN MONOID
Abstract We characterise the elements of the (maximum) idempotent-generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated with certain normal forms. We also calculate
Variants of finite full transformation semigroups
  • I. Dolinka, J. East
  • Mathematics, Computer Science
    Int. J. Algebra Comput.
  • 20 October 2014
TLDR
The rank and idempotent rank (if applicable) of each semigroup, and the number of (idempotent) generating sets of the minimal possible size are calculated.
The Bergman property for endomorphism monoids of some Fra
Based on an idea of Y. P\'eresse and some results of Maltcev, Mitchell and Ru\v{s}kuc, we present sufficient conditions under which the endomorphism monoid of a countably infinite ultrahomogeneous
Every Group is a Maximal Subgroup of the Free Idempotent Generated Semigroup over a band
TLDR
Given an arbitrary group G, it is shown that the free idempotent generated semigroup over BG has a maximal subgroup isomorphic to G, and if G is finitely presented then BG is finite.
A characterization of retracts in certain Fraïssé limits
  • I. Dolinka
  • Mathematics, Computer Science
    Math. Log. Q.
  • 1 February 2012
Assuming certain conditions on a class of finitely generated first-order structures admitting the model-theoretical construction of a Fraisse limit, we characterize retracts of such limits as
A Note on Free Idempotent Generated Semigroups over the Full Monoid of Partial Transformations
Recently, Gray and Ru\v skuc proved that if e is a rank k idempotent transformation of the set {1,…, n} to itself and k ≤ n − 2, then the maximal subgroup of the free idempotent generated semigroup
Sandwich semigroups in diagram categories
This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley–Lieb categories. If [Formula: see text] denotes any of these
Enumeration of idempotents in diagram semigroups and algebras
On Equations for Union-Free Regular Languages
TLDR
This paper considers the variety UF generated by all algebras of binary relations equipped with the operations of composition, reflexive-transitive closure, and the empty set and the identity relation as constants, and shows that it is not finitely based.
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