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Free products of inverse semigroups II

  • Peter R. Jones (a1), Stuart W. Margolis (a2), John Meakin (a3) and Joseph B. Stephen (a4)

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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.

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References

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1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vol. I (American Mathematical Society, 1961).
2.Hopcroft, J. E. and Ullman, J. D., Introduction to automata theory, languages and computation (Addison Wesley, 1979).
3.Jones, P. R., A graphical representation for the free product of E-unitary inverse semigroups, Semigroup Forum 24 (1982), 195221.
4.Jones, P. R., Free products of inverse semigroups, Trans. Amer. Math. Soc. 282 (1984), 293317.
5.Knox, N., On the inverse semigroup coproduct of an arbitrary collection of groups (Ph.D. thesis, Tennessee State University, 1974).
6.McAlister, D. B., Inverse semigroups generated by a pair of subgroups, Proc. Roy. Soc. Edinburgh Sect. A 77 (1976), 922.
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), 4576.
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), 89103.
9.Munn, W. D., Free inverse semigroups, Proc. London Math. Soc. (3) 29 (1974), 385404.
10.Petrich, M., Inverse semigroups (Wiley, 1984).
11.Stallings, J. R., Topology of finite graphs, Invent. Math. 71 (1983), 551565.
12.Stephen, J. B., Presentations of inverse monoids, J. Pure Appl. Algebra 63 (1990), 81112.
13.Stephen, J. B., Applications of automata theory to presentations of monoids and inverse monoids (Ph.D. thesis, University of Nebraska, 1987).

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Free products of inverse semigroups II

  • Peter R. Jones (a1), Stuart W. Margolis (a2), John Meakin (a3) and Joseph B. Stephen (a4)

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