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Complete \(\ell\)-groupoids and their prime spectra. (English. Russian original) Zbl 0936.06004

Algebra Logika 36, No. 3, 341-355 (1997); translation in Algebra Logic 36, No. 3, 204-211 (1997).
We discuss the validity of the infinite \(\cap\)-distributivity law in a lattice of radical elements of an arbitrary complete \(\ell\)-groupoid, in particular, in the lattice of radical ideals of an arbitrary ring. The notion of a prime spectrum \(\text{Spec}(L)\) is defined and a specific place is indicated that that topological spaces of type \(\text{Spec}(L)\) occupy among all \(T_0\)-spaces.

MSC:

06B15 Representation theory of lattices
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
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