Geodesic
Free products of inverse semigroups II
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 373-387

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

Let S and T be inverse semigroups. Their free product S inv T is their coproduct in the category of inverse semigroups, defined by the usual commutative diagram. Previous descriptions of free products have been based, like that for the free product of groups, on quotients of the free semigroup product S sgp T. In that framework, a set of canonical forms for S inv T consists of a transversal of the classes of the congruence associated with the quotient. The general result [4] of Jones and previous partial results [3], [5], [6] take this approach. 
Jones, Peter R.; Margolis, Stuart W.; Meakin, John; Stephen, Joseph B. Free products of inverse semigroups II. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 373-387. doi: 10.1017/S0017089500008442
@article{10_1017_S0017089500008442,
     author = {Jones, Peter R. and Margolis, Stuart W. and Meakin, John and Stephen, Joseph B.},
     title = {Free products of inverse semigroups {II}},
     journal = {Glasgow mathematical journal},
     pages = {373--387},
     year = {1991},
     volume = {33},
     number = {3},
     doi = {10.1017/S0017089500008442},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008442/}
}
TY  - JOUR
AU  - Jones, Peter R.
AU  - Margolis, Stuart W.
AU  - Meakin, John
AU  - Stephen, Joseph B.
TI  - Free products of inverse semigroups II
JO  - Glasgow mathematical journal
PY  - 1991
SP  - 373
EP  - 387
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008442/
DO  - 10.1017/S0017089500008442
ID  - 10_1017_S0017089500008442
ER  - 
%0 Journal Article
%A Jones, Peter R.
%A Margolis, Stuart W.
%A Meakin, John
%A Stephen, Joseph B.
%T Free products of inverse semigroups II
%J Glasgow mathematical journal
%D 1991
%P 373-387
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500008442/
%R 10.1017/S0017089500008442
%F 10_1017_S0017089500008442

[1] 1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vol. I (American Mathematical Society, 1961). Google Scholar

[2] 2.Hopcroft, J. E. and Ullman, J. D., Introduction to automata theory, languages and computation (Addison Wesley, 1979). Google Scholar

[3] 3.Jones, P. R., A graphical representation for the free product of E-unitary inverse semigroups, Semigroup Forum 24 (1982), 195–221. Google Scholar

[4] 4.Jones, P. R., Free products of inverse semigroups, Trans. Amer. Math. Soc. 282 (1984), 293–317. Google Scholar | DOI

[5] 5.Knox, N., On the inverse semigroup coproduct of an arbitrary collection of groups (Ph.D. thesis, Tennessee State University, 1974). Google Scholar

[6] 6.McAlister, D. B., Inverse semigroups generated by a pair of subgroups, Proc. Roy. Soc. Edinburgh Sect. A 77 (1976), 9–22. Google Scholar | DOI

[7] 7.Margolis, S. W. and Meakin, J., E-unitary inverse monoids and the Cayley graph of a group presentation, J. Pure Appl. Algebra 58 (1989), 45–76. Google Scholar | DOI

[8] 8.Meakin, J., Automata and the word problem, in Pin, J. E. (ed.), Formal properties of finite automata and applications, Lecture Notes in Comput. Sci. 386 (1989), 89–103. Google Scholar | DOI

[9] 9.Munn, W. D., Free inverse semigroups, Proc. London Math. Soc. (3) 29 (1974), 385–404. Google Scholar | DOI

[10] 10.Petrich, M., Inverse semigroups (Wiley, 1984). Google Scholar

[11] 11.Stallings, J. R., Topology of finite graphs, Invent. Math. 71 (1983), 551–565. Google Scholar

[12] 12.Stephen, J. B., Presentations of inverse monoids, J. Pure Appl. Algebra 63 (1990), 81–112. Google Scholar | DOI

[13] 13.Stephen, J. B., Applications of automata theory to presentations of monoids and inverse monoids (Ph.D. thesis, University of Nebraska, 1987). Google Scholar

Cité par Sources :