Free products of inverse semigroups

Author:
Peter R. Jones

Journal:
Trans. Amer. Math. Soc. **282** (1984), 293-317

MSC:
Primary 20M05

DOI:
https://doi.org/10.1090/S0002-9947-1984-0728714-X

MathSciNet review:
728714

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Abstract: A structure theorem is provided for the free product of inverse semigroups and . Each element of is uniquely expressible in the form , where is a certain finite set of ``left reduced'' words and either or is a ``reduced'' word with . (The word in is called reduced if no letter is idempotent, and left reduced if exactly is idempotent; the notation stands for .) Under a product remarkably similar to Scheiblich's product for free inverse semigroups, the corresponding pairs form an inverse semigroup isomorphic with .

This description enables various properties of to be determined. For example is always completely semisimple and each of its subgroups is isomorphic with a finite subgroup of or . If neither nor has a zero then is fundamental, but in general fundamentality itself is not preserved.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0728714-X

Keywords:
Inverse semigroup,
free product,
canonical form,
structural and preservational properties

Article copyright:
© Copyright 1984
American Mathematical Society