Completel-groupoids and their prime spectra

We argue for the validity of the infinite ∩-distributivity law in a lattice of radical elements of an arbitrary complete l-groupoid, in particular, in the lattice of radical ideals of an arbitrary ring. The notion of a prime spectrumSpec (L) is defined, and we point out a specific place that topological spaces of typeSpec (L) hold among all T_o-spaces. Supported by the AMS grant. Translated fromAlgebra i logika, Vol. 36, No. 3, pp. 341–355, May–June, 1997.