Abstract
In this paper, we give a direct proof that every strongly \(\user1{E}^ * --\user1{unitary}\) inverse semigroup can be embedded into a 0-semidirect product of a semilattice with zero by a group. As a corollary, we obtain a new proof of the structure theory of strongly \(\user1{E}^ * --\user1{unitary}\) inverse semigroups described in [1]. We also prove that the strongly \(\user1{E}^ * --\user1{unitary}\) inverse semigroups are precisely \(\user1{E}^ * -\user1{unitary}\) inverse semigroups equipped with a \(\user1{0 - restricted}\), idempotent pure prehomomorphism to a primitive inverse semigroup.
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Jiang, Z. Some notes on strongly E*-unitary inverse semigroups. Periodica Mathematica Hungarica 44, 75–80 (2002). https://doi.org/10.1023/A:1014975919205
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DOI: https://doi.org/10.1023/A:1014975919205