# The Immersibility of a Semigroup into a Group

@article{Lambek1951TheIO, title={The Immersibility of a Semigroup into a Group}, author={Joachim Lambek}, journal={Canadian Journal of Mathematics}, year={1951}, volume={3}, pages={34 - 43} }

A semigroup is a set of elements which is closed under an associative operation, usually called multiplication. When can a semigroup be embedded in a group, i.e., under what condition is it isomorphic to a subset of a group? A necessary condition for immersibility is clearly the so-called cancellation law:

## 24 Citations

The Embedding Theorems of Malcev and Lambek

- MathematicsCanadian Journal of Mathematics
- 1963

A given semigroup is said to be embeddable in a group if there exists a group which contains a subsemigroup isomorphic to . It can easily be proved that cancellation is a necessary condition for…

A GENERALIZATION OF ADJAN'S THEOREM ON EMBEDDINGS OF SEMIGROUPS

- Mathematics
- 2013

In this paper we investigate the question of possibility to injectively map a semigroup into a group. Adjan's theorem provides a sufficient condition for such a map to exist for semigroups with…

Embedding of rings

- Mathematics
- 1987

CONTENTS Introduction § 1. Embedding of semigroups in groups § 2. A problem of A.I. Mal'tsev § 3. Homomorphisms from rings into (skew) fields, and non-commutative localization § 4. Rings of…

Malcev sequences and associative symmetrisations

- Mathematics
- 1984

Cancellativity is a necessary and sufficient condition for a semigroup S to be symmetrisable; that is, for S to be embeddable in a partial multiplicative system, called a symmetrisation of S, which…

Relation algebras and function semigroups

- Mathematics
- 1970

The concept of relation algebra unifies many familiar notions from algebra (especially those of systems having “natural” models as groups, Boolean algebras etc.). The fundamental theorem on relation…

The embeddability of a semigroup—Conditions common to Mal’cev and Lambek

- Mathematics
- 1971

Two systems of conditions-due to Mal'cev and to Lambek-are known to be necessary and sufficient for a semigroup to be embeddable in a group. This paper shows by means of an example that the…

The Early Development of the Algebraic Theory of Semigroups

- Mathematics
- 2009

In the history of mathematics, the algebraic theory of semigroups is a relative new-comer, with the theory proper developing only in the second half of the twentieth century. Before this, however,…

Embedding semigroups in groups: not as simple as it might seem

- Mathematics
- 2014

We consider the investigation of the embedding of semigroups in groups, a problem which spans the early-twentieth-century development of abstract algebra. Although this is a simple problem to state,…

Embedding of rings

- Mathematics
- 1987

CONTENTSIntroduction ??1. Embedding of semigroups in groups ??2. A problem of A.I. Mal'tsev ??3. Homomorphisms from rings into (skew) fields, and non-commutative localization ??4. Rings of fractions.…

Presentations for subsemigroups of groups

- Mathematics
- 2005

This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a…

## References

SHOWING 1-4 OF 4 REFERENCES

On the immersion of an algebraic ring into afield, Math

- Ann., vol
- 1937

Ûber die Einbettung von assoziativen Systemen in Gruppen

- Mat. Sbornik
- 1940

JJber die Einbettung von assoziativen Systemen in Gruppen

- Mat. Sbornik
- 1939