scholarly journals Lattice isomorphisms of free products of inverse semigroups

1984 ◽  
Vol 89 (2) ◽  
pp. 280-290 ◽  
Author(s):  
Peter R Jones
Keyword(s):  
Inverse Semigroups ◽  
Free Products

Residual finiteness of free products of combinatorial strict inverse semigroups

1994 ◽  
Vol 124 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Inverse Semigroups ◽  
Residual Finiteness ◽  
Free Products ◽  
Residually Finite

It is shown that the free product of two residually finite combinatorial strict inverse semigroups in general is not residually finite. In contrast, the free product of a residually finite combinatorial strict inverse semigroup and a semilattice is residually finite.

Free products amalgamating unitary subsemigroups

1976 ◽  
Vol 15 (1) ◽  
pp. 117-124 ◽  
Author(s):  
G.B. Preston
Keyword(s):  
Free Product ◽  
Inverse Semigroups ◽  
Free Products ◽  
Short Method

Let Si, i ∈ I, be a set of semigroups such that Si ∩ Sj = U, if i ≠ j, and such that U is a unitary subsemi-group of Si for each i in I. The semigroup amalgam [{Si | i ∈ I}; U] determined by this system is the partial groupoid G = USi in which a product of two elements is defined if and only if they both belong to the same Si and their product is then taken as their product in Si. In 1962, J.M. Howie showed that the amalgam G is embeddable in the free product of the Si, amalgamating U. To prove this result it suffices to find any semigroup in which G can be embedded. In this paper, by taking convenient representations of the Si, adapting a method recently (1975) used by T.E. Hall for inverse semigroups, we provide a short method of constructing such a semigroup.

A note on primeness of semigroup rings

1992 ◽  
Vol 120 (3-4) ◽  
pp. 191-197 ◽  
Author(s):  
Pedro V. Silva
Keyword(s):  
Inverse Semigroups ◽  
Semigroup Rings ◽  
Free Products ◽  
Infinite Rank

SynopsisThis note discusses primeness for semigroup rings of semigroups satisfying a certain condition, weaker than the u.p. property. These semigroups include free products of semigroups, semigroups presented by a single relator and at least three generators, and free inverse semigroups of infinite rank.

scholarly journals Free products of inverse semigroups II

1991 ◽  
Vol 33 (3) ◽  
pp. 373-387 ◽  
Author(s):  
Peter R. Jones ◽  
Stuart W. Margolis ◽  
John Meakin ◽  
Joseph B. Stephen
Keyword(s):  
Free Product ◽  
General Result ◽  
Commutative Diagram ◽  
Free Semigroup ◽  
Inverse Semigroups ◽  
Canonical Forms ◽  
Free Products ◽  
Free Product Of Groups ◽  
Product Of Groups

Let S and T be inverse semigroups. Their free product S inv T is their coproduct in the category of inverse semigroups, defined by the usual commutative diagram. Previous descriptions of free products have been based, like that for the free product of groups, on quotients of the free semigroup product S sgp T. In that framework, a set of canonical forms for S inv T consists of a transversal of the classes of the congruence associated with the quotient. The general result [4] of Jones and previous partial results [3], [5], [6] take this approach.

scholarly journals The Hope property and free products of semigroups

1979 ◽  
Vol 27 (3) ◽  
pp. 358-364 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Free Product ◽  
Inverse Semigroups ◽  
Free Products ◽  
Elementary Methods

AbstractThe free product of two Hopfian groups (in the category of groups) need not be Hopfian. We prove, by elementary methods, that the free product of two simple Hopfian inverse semigroups is Hopfian. In particular the free product of any two Hopfian groups, in the category of inverse semigroups, is again Hopfian. In fact the same is true in the category of all semigroups.

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