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Lattice isomorphisms of modular inverse semigroups

Published online by Cambridge University Press:  13 July 2011

K. G. Johnston
K. G. Johnston
Affiliation:
Department of MathematicsCollege of CharlestonCharleston, SC 29424, U.S.A.
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For an inverse semigroup S we will consider the lattice of inverse subsemigroups of S, denoted L(S). A major problem in algebra has been that of finding to what extent an algebra is determined by its lattice of subalgebras. (See, for example, the survey article [9]). By a lattice isomorphism (L-isomorphism, structural isomorphism, or projectivity) of an inverse semigroup S onto another T we shall mean an isomorphism Φ of L(S) onto L(T). A mapping φ from S to T is said to induce Φ if AΦ = Aφ for all A in L(S). We say that S is strongly determined by L(S) if every lattice isomorphism of S onto T is induced by an isomorphism of S onto T.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 441 - 446
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Howie, J. M., An Introduction to Semigroup Theory (Academic Press, London, 1976).Google Scholar
2.Johnston, K. G. and Jones, P. R., Modular inverse semigroups, J. Austral. Math. Soc. Ser. A, to appear.Google Scholar
3.Jones, P. R., Semimodular inverse semigroups, J. London Math. Soc. 17 (1978), 446–456.CrossRefGoogle Scholar
4.Jones, P. R., Distributive inverse semigroups, J. London Math. Soc. 17 (1978), 457–466.CrossRefGoogle Scholar
5.Jones, P. R., Lattice isomorphisms of distributive inverse semigroups, Quart. J. Math. Oxford 30 (1979), 301–314.Google Scholar
6.Jones, P. R., Inverse semigroups determined by their lattices of inverse subsemigroups, J. Austral. Math. Soc. Ser. A 30 (1981), 321–346.Google Scholar
7.Miller, D. D. and Clifford, A. H., Regular D-classes in semigroups, Trans. Amer. Math. Soc. 82 (1956), 270–280.Google Scholar
8.Petrich, M., Inverse Semigroups (Wiley, New York, 1984).Google Scholar
9.Sevrin, L. N. and Ovsyannikov, A. J., Semigroups and their subsemigroup lattices, Semigroup Forum 27 (1983), 1–154.CrossRefGoogle Scholar