Semidegenerate Congruence-modular Algebras Admitting a Reticulation

The reticulation L(R) of a commutative ring R was introduced by Joyal in 1975, then the theory developed Simmons remarkable paper published 1980. is bounded distributive algebra whose main property that Zariski prime spectrum Spec(R) and Stone SpecId (L(R)) are homeomorphic. construction lattice generalized Belluce for each unital defined axioms. In recent we algebras semidegenerate congruence-modular variety V. For any A ∈ V L(A), but general Spec(A) not homeomorphic with (L(A)). We quasi-commutative (as generalization Belluce’s rings) proved V, spectra (L(A)) this define four axioms prove two reticulations isomorphic lattices. By using uniqueness other results from mentioned paper, obtain characterization theorem admit reticulation: if only admits reticulation. This result universal following theorem: Another subject treated spectral closure an notion generalizes ring.