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55
Inverse subsemigroups of the monogenic free inverse semigroup
"... problem It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proved to be decidable. 1 ..."
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problem It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proved to be decidable. 1
Inverse semigroups determined by their lattices of convex inverse subsemigroups II
 ALGEBRA UNIVERSALIS
, 2002
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LARGEST 2GENERATED SUBSEMIGROUPS OF THE SYMMETRIC INVERSE SEMIGROUP
, 2006
"... The symmetric inverse monoid In is the set of all partial permutations of an nelement set. The largest possible size of a 2generated subsemigroup of In is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)/In  → 1 as ..."
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The symmetric inverse monoid In is the set of all partial permutations of an nelement set. The largest possible size of a 2generated subsemigroup of In is determined. Examples of semigroups with these sizes are given. Consequently, if M(n) denotes this maximum, it is shown that M(n)/In  → 1
Largest subsemigroups of the full transformation monoid
, 2008
"... In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T ≤ S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappi ..."
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of mappings. The subsemigroups T that we consider are of one of the following types: left zero, right zero, completely simple, or inverse. Furthermore, we find the largest size of such subsemigroups U where the least rank of an element in U is specified. Numerous examples are given.
HNN extensions of inverse semigroups and groupoids
"... We use the isomorphism between the categories of inverse semigroups and inductive groupoids to construct HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base. Properties of groupoids then ensure that the base inverse semigroup always embed ..."
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We use the isomorphism between the categories of inverse semigroups and inductive groupoids to construct HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base. Properties of groupoids then ensure that the base inverse semigroup always
On the lattice of full eventually regular subsemigroups
"... Abstract We generalize to eventually regular (or 'πregular') semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full e ..."
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Abstract We generalize to eventually regular (or 'πregular') semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full
Lower semimodular inverse semigroups, II
, 2010
"... The description by the authors of the inverse semigroups S for which the lattice LF(S) of full inverse subsemigroups is lower semimodular is used to describe those for which (a) the lattice L(S) of all inverse subsemigroups or (b) the lattice Co (S) of convex inverse subsemigroups has that property ..."
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The description by the authors of the inverse semigroups S for which the lattice LF(S) of full inverse subsemigroups is lower semimodular is used to describe those for which (a) the lattice L(S) of all inverse subsemigroups or (b) the lattice Co (S) of convex inverse subsemigroups has
The Lattices of Group Fuzzy Congruences and Normal Fuzzy Subsemigroups on Inversive Semigroups
"... The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in inversive semigroups. Moreover, we show that the set of group fuzz ..."
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The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in inversive semigroups. Moreover, we show that the set of group
Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup
, 2009
"... We prove that the minimal cardinality of the semitransitive subsemigroup in the singular part In \ Sn of the symmetric inverse semigroup In is 2n −p+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality. 1 ..."
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We prove that the minimal cardinality of the semitransitive subsemigroup in the singular part In \ Sn of the symmetric inverse semigroup In is 2n −p+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality. 1
On lattice isomorphisms of inverse semigroups
 Glasgow Math. J
, 2004
"... An Lisomorphism between inverse semigroups S and T is an isomorphism between their lattices L(S) and L(T) of inverse subsemigroups. The author and others have shown that if S is aperiodic – has no nontrivial subgroups – then any such isomorphism Φ induces a bijection φ between S and T. We first cha ..."
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Cited by 5 (3 self)
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An Lisomorphism between inverse semigroups S and T is an isomorphism between their lattices L(S) and L(T) of inverse subsemigroups. The author and others have shown that if S is aperiodic – has no nontrivial subgroups – then any such isomorphism Φ induces a bijection φ between S and T. We first
Results 1  10
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55