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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).

06F05 Ordered semigroups and monoids
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