## 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.)