Totally Ordered Commutative Semigroups

@inproceedings{Clifford2007TotallyOC,
  title={Totally Ordered Commutative Semigroups},
  author={Alison H Clifford},
  year={2007}
}
Let 5( + , < ) be a system consisting of a set S endowed with an associative binary operation + and a total ( = linear = simple) order relation < . The composition + and the relation < may be connected by either or both of the following conditions. MC (Monotone Condition). If a and b are elements of 5 such that a<b then a+c^b+c and c+a^c+b for all c in S. CC (Continuity Condition), (x, y)—>x+y is a continuous mapping of 5 X 5 into 5, where 5 is endowed with the order topology. We shall call S… CONTINUE READING

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 39 extracted citations

On a class of conjunctive left-continuous uninorms

2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD) • 2017
View 4 Excerpts
Highly Influenced

Uninorms - State of the art with recent results

2011 IEEE 12th International Symposium on Computational Intelligence and Informatics (CINTI) • 2011
View 10 Excerpts
Highly Influenced

On group-like FLe-algebras

2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) • 2015
View 3 Excerpts
Highly Influenced

Hahn-type embedding theorem for a class of residuated chains

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) • 2017

References

Publications referenced by this paper.
Showing 1-10 of 18 references

On the structure of semigroups on a compact manifold with boundary

Paul S. Mostert, Allen L. Shields
Ann. of Math. vol • 1957
View 5 Excerpts
Highly Influenced

Naturally totally ordered commutative semigroups, Amer

A. H. Clifford
J. Math, vol • 1954
View 4 Excerpts
Highly Influenced

Partially ordered abelian semigroups I. On the extension of the strong partial order defined on abelian semigroups

O. Nakada
J. Fac. Sci. Hokkaido Univ. vol • 1951
View 5 Excerpts
Highly Influenced

Über gewisse Halbverbande und kommutative

F. Klein-Barmen
Semigruppen II, Math. Z. vol • 1942
View 4 Excerpts
Highly Influenced

Regularly totally ordered semigroups I

M. Yamada
Science Reports of Shimane University, • 1957
View 3 Excerpts
Highly Influenced

Caractérisation des semi-groupes à un paramètre

Dov Tamari
C. R. Acad. Sci. Paris vol • 1949
View 4 Excerpts
Highly Influenced

Gleason , Arcs in locally compact groups

M. Andrew
Proc . Nat . Acad . Sci . • 1955

The structure of topological semigroups

A. D. Wallace
Bull. Amer. Math. Soc. vol • 1955
View 2 Excerpts

On an ordered semigroup

C. G. Chehata
J. London Math. Soc. vol • 1953
View 1 Excerpt

On the theory of ordered semigroups, Ivanov. Gos

A. A. Vinogradov
Ped. Inst. Uö. Zap. Fiz.-Mat. Nauki, • 1953
View 1 Excerpt

Similar Papers

Loading similar papers…