For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free ...inverse. We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines.
We study growth of inverse semigroups defined by finite presentations. Let
S
be a finitely presented Rees quotient of a free inverse semigroup given by an irredundant presentation with
n
generators ...and
m
relators. We show that if
S
has polynomial growth, then
m
≥
n
2
-
1
and this estimate is sharp. For any positive integer
n
, we also find, up to isomorphism, syntactic descriptions of all presentations that achieve this sharp lower bound. As part of the process, we describe all irredundant presentations of finite Rees quotients of free inverse semigroups having rank
n
, with the smallest number, namely
n
2
, of relators.
We prove that automorphisms of the endomorphism semigroup of a free inverse semigroup are inner and determine all isomorphisms between the endomorphism semigroups of free inverse semigroups.
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 proven to be decidable.
Free Inverse Semigroups Scheiblich, H. E.
Proceedings of the American Mathematical Society,
01/1973, Letnik:
38, Številka:
1
Journal Article
Recenzirano
Odprti dostop
At least three authors have offered proofs of the existence of a free inverse semigroup, but without describing its structure. This paper shows that if X is a nonempty set, G is the group on X, and E ...is a certain subsemilattice of the power set of G, then a certain collection of principal ideal isomorphisms of E is a free inverse semigroup on X.
An inverse semigroup T is separated over a subsemigroup S if T is generated, as an inverse semigroup, by S and for each a, b ε S there exists x ε Sa ∩ Sb such that a-1ab-1b = x-1x and dually for ...right ideals. For example, if T is generated as an inverse semigroup by a semigroup S whose principal left and right ideals form chains under inclusion, then T is separated over S. In this paper we investigate the structure of inverse semigroups T which are separated over subsemigroups S.
Conjugacy in inverse semigroups Araújo, João; Kinyon, Michael; Konieczny, Janusz
Journal of algebra,
09/2019, Letnik:
533
Journal Article
Recenzirano
Odprti dostop
In a group G, elements a and b are conjugate if there exists g∈G such that g−1ag=b. This conjugacy relation, which plays an important role in group theory, can be extended in a natural way to inverse ...semigroups: for elements a and b in an inverse semigroup S, a is conjugate to b, which we will write as a∼ib, if there exists g∈S1 such that g−1ag=b and gbg−1=a. The purpose of this paper is to study the conjugacy ∼i in several classes of inverse semigroups: symmetric inverse semigroups, McAllister P-semigroups, factorizable inverse monoids, Clifford semigroups, the bicyclic monoid, stable inverse semigroups, and free inverse semigroups.
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