2026/06/30 by Peyman Nasehpour · 1 citation
#math.AC #math.RA
We introduce the overflow semiring S = A \uplusord L, extending a positive information algebra A by a join-semilattice L, where elements of L dominate A and arithmetic in L reduces to the join. This models overflow in computational systems and generalizes the transition from finite to infinite cardinal arithmetic. We characterize the idempotent elements of S and S[X], fully classify idempotent power series over cardinal numbers, describe the structure of prime and maximal ideals, compute the Krull dimension of S (dim S = dim A + |L| for well-ordered finite L), and establish Noetherian and Artinian criteria.