• Corpus ID: 252567780

Abelianness and centrality in inverse semigroups

@inproceedings{Kinyon2022AbeliannessAC,
  title={Abelianness and centrality in inverse semigroups},
  author={Michael K. Kinyon and David Stanovsk'y},
  year={2022}
}
. We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of the corresponding congruence pairs. We relate centrality to conjugation in inverse semigroups. Subsequently we prove that solvable and nilpotent inverse semigroups are groups. 
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References

SHOWING 1-10 OF 30 REFERENCES

Fundamentals of semigroup theory

1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free…

The conjugate hull of an inverse semigroup

  • M. Petrich
  • Mathematics
    Glasgow Mathematical Journal
  • 1980
There is a large body of literature on inverse semigroups. This literature contains a considerable amount of information concerning congruences on these semigroups, which is not surprising in view of…

Abelian Extensions and Solvable Loops

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known…

Solvability and the permutation property in inverse semigroups

If any product of three elements of an inverse semigroup S can be re-ordered, then S is solvable; the same is not true for any integer number greater than three.

The rank of variants of nilpotent pseudovarieties

COMMUTATOR THEORY WITHOUT JOIN-DISTRIBUTIVITY

We develop Commutator Theory for congruences of general alge- braic systems (henceforth called algebras) assuming only the existence of a ternary term d such that d(a, b, b)(a, a)a(a, a)d(b, b, a),…

Groupoids

This paper gives some new results for the theory of quantum groupoids. First, the authors recall the relevant notions and results of the theory of Li-Rinehart algebras and bialgebras. Then, they…

Commutator theory for loops

Nilpotent inverse semigroups with central idempotents

An inverse semigroup S with central idempotents, i.e. a strong semilattice of groups, will be called nilpotent, if it is finite and if for each prime divisor p¡ of the orders of the structure groups…

Commutator theory for congruence modular varieties

Introduction In the theory of groups, the important concepts of Abelian group, solvable group, nilpotent group, the center of a group and centraliz-ers, are all defined from the binary operation [x,…