FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 2, PAGES 627-632

**Atomic theories of residuated semigroup families**

M. R. Pentus

Abstract

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A residuated semigroup is a partially ordered semigroup together with
two binary operations $\backslash $ and $/$, such that the assertions
$a$£ c/b,
$a$× b
£ c,
and $b$£ a \ c are equivalent.
We formulate a necessary and sufficient condition for an arbitrary set
of atomic formulas of the signature $\{$£,
×, \, / }
to be the atomic theory of some residuated
semigroup family.
We also consider some specific residuated semigroups and residuated
semigroup families.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k00/k002/k00220h.htm

Last modified: September 1, 2000