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.

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Last modified: September 1, 2000