Geodesic
An embedding theorem with amalgamation for cancellative semigroups†
Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 19-26

Voir la notice de l'article provenant de la source Cambridge University Press

Let {Si; i ε I} be a finite or infinite family of cancellative semigroups. Let U be a cancellative semigroup, and suppose that there exists, for each i in I, a monomorphism φi: u→ Si. We are interested in finding a semigroup T with the following properties.(a) For each i in I, there is a monomorphism λi: Si → T such that uφiλi = uøjλi for all u ɛ U and all i, j in I. That is to say, there exists a monomorphism λ: U → T which equals øiλi for all i in I.Siλi∩Sjλj = Uλ (i, j ε I; i ≠ j). 
Howie, J. M. An embedding theorem with amalgamation for cancellative semigroups†. Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 19-26. doi: 10.1017/S204061850003464X
@article{10_1017_S204061850003464X,
     author = {Howie, J. M.},
     title = {An embedding theorem with amalgamation for cancellative semigroups{\textdagger}},
     journal = {Glasgow mathematical journal},
     pages = {19--26},
     year = {1963},
     volume = {6},
     number = {1},
     doi = {10.1017/S204061850003464X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S204061850003464X/}
}
TY  - JOUR
AU  - Howie, J. M.
TI  - An embedding theorem with amalgamation for cancellative semigroups†
JO  - Glasgow mathematical journal
PY  - 1963
SP  - 19
EP  - 26
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S204061850003464X/
DO  - 10.1017/S204061850003464X
ID  - 10_1017_S204061850003464X
ER  - 
%0 Journal Article
%A Howie, J. M.
%T An embedding theorem with amalgamation for cancellative semigroups†
%J Glasgow mathematical journal
%D 1963
%P 19-26
%V 6
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S204061850003464X/
%R 10.1017/S204061850003464X
%F 10_1017_S204061850003464X

[1] 1Birkhoff, G., Lattice theory (Foreword on Algebra), Revised Edition, Amer. Math. Soc. Colloquium publications XXV (New York, 1948). Google Scholar

[2] 2Dubreil, P., Contribution à la théorie des demigroupes, Mem. Acad. Sci. Inst. France 63 (1941), no. 3, 1–52. Google Scholar

[3] 3Hall, M., The theory of groups, (New York, 1959). Google Scholar

[4] 4Howie, J. M., Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511–534. Google Scholar | DOI

[5] 5Howie, J. M., Some problems in the theory of semigroups, Thesis, Oxford (1961). Google Scholar

[6] 6Kurosh, A. G., The theory of groups, vol. II, (New York, 1955), 29–32. Google Scholar

[7] 7Levi, F. W., On semigroups, Bull. Calcutta Math. Soc. 36 (1944), 141–146. Google Scholar

Cité par Sources :