Free distributive structures over general algebras (Q2759834)

In the first part of this paper the author constructs universal join-distributive structures (\(m\)-semilattices, prequantales and generalizations of them, so-called \(m\)-\(\mho\)-semilattices) over \(m\)-\(\mho\)-algebras, i.e., arbitrary algebras of a (not necessarily finitary) type with an extra binary operation \(m\), by means of so-called strong lower ideals (sl-ideals). Sl-ideals containing with \(a^2\) also the element \(a\) itself are called sl-radicals. Finally, the author shows that the radical of an sl-ideal consists of all elements having a suitable dyadic power in a given ideal; the Prime Ideal Theorem for Boolean algebras is equivalent to the representation of sl-radicals as intersections of prime sl-ideals (in finitary \(m\)-\(\mho\)-algebras).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00014].