FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 1, PAGES 87-103
A. Ja. Ovsyannikov
Abstract
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A lattice isomorphism $\psi$ of a semigroup $S$ upon a semigroup $T$
is called an \emph{ideal lattice isomorphism} if it induces a bijection
of the set of ideals of $S$ onto the corresponding set of $T$ .
\emph{Left} and \emph{right ideal lattice isomorphisms} are defined
in a similar way. The order on idempotents and the property of being
a subgroup are proved to retain under lattice isomorphisms of these
kinds. The property of a semigroup of being decomposable in a semilattice
of Archimedean semigroups is retained as well. Mappings that induce ideal
lattice isomorphisms of idempotent semigroups are described.
In particular, each left ideal or right ideal lattice isomorphism of
an idempotent semigroup is induced by an isomorphism.
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Last modified: May 10, 2001