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Minimal prime ideals in autometrized algebras. (English) Zbl 0814.06011
An autometrized \(\ell\)-algebra is a lattice-ordered commutative monoid \(A\) with an additional binary operation on \(A\) satisfying the properties of a metric. The author shows some connections between prime ideals of \(A\) and prime filters on the positive cone \(A^ +\), and between prime ideals and polars of \(A\), where \(A\) belongs to a special class of autometrized \(\ell\)-algebras (including Brouwerian algebras and commutative \(\ell\)-groups). Many of the properties of minimal prime ideals and polars are strengthened for dually residuated \(\ell\)- semigroups, which include Boolean algebras and commutative \(\ell\)-groups.

MSC:
06F05 Ordered semigroups and monoids
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References:
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