On ring-like structures of lattice-Ordered numerical events

Let [Formula: see text] be a set of states physical system. The probabilities the occurrence an event when system is in different define function from to called numerical or, more accurately, text]-probability. Sets text]-probabilities ordered by partial order functions give rise so-called algebras text]-probabilities, particular, ones that are lattice-ordered. Among these, there text]-algebras known probability theory and Hilbert-space logics which important quantum-mechanics. Any algebra can serve as quantum-logic, it special interest this logic turns out Boolean because then observed will classical. one-to-one correspondence rings, question arises find analogue for lattice-ordered generalizing between rings. We answer defining ring-like structures events (RLSEs). First, structure RLSEs revealed rings among characterized. Then we establish how correspond events. Further, associating studied. It shown only two ways assign if one restricts corresponding mappings term over underlying orthomodular lattice. These very also assigned