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Regular ideals in autometrized algebras. (English) Zbl 0738.06014
A partially ordered commutative semigroup $$A$$ with zero is called an autometrized algebra if a binary operation is defined on $$A$$ behaving like a metric (this concept was introduced by K. L. Swamy [Math. Ann. 157, 65–74 (1964; Zbl 0135.02602)]). The notion of an ideal in $$A$$ is defined (respecting the metric) and several types of ideals in different classes of autometrized algebras are studied. It is shown that there are connections between regular and prime ideals if $$A$$ satisfies certain conditions (it would be too complicated to reproduce all the definitions here).

MSC:
 06F05 Ordered semigroups and monoids
References:
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