FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 87-103

**Ideal lattice isomorphisms of semigroups**

A. Ja. Ovsyannikov

Abstract

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A lattice isomorphism $$y of a
semigroup $S$ upon a
semigroup $T$ is called
an *ideal lattice isomorphism* if it induces
a bijection of the set of ideals of $S$ onto
the corresponding set of $T$.
*Left* and *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.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k01/k011/k01106h.htm

Last modified: May 10, 2001