The Chinese Remainder Theorem for Strongly Semisimple MV-Algebras and Lattice-Groups

The Chinese Remainder Theorem

A Representation Theorem for MV-algebras

An MV-pair is a pair (B, G) where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain conditions. Let ∼G be the equivalence relation on B naturally associated with G. We prove that for every MV-pair (B, G), the effect algebra B/ ∼G is an MV-effect algebra. Moreover, for every MV-effect algebra M there is an MV-pair (B, G) such that M is isomorphic to B/ ∼G.

Robustness in Chinese Remainder Theorem

Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reco...

A Spectral Theorem for Sigma Mv-algebras

MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for "multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis-Sikorski theorem for cr-MV-algebras, we prove that, with every element a in a cr-MV alge...

A Multivariable Chinese Remainder Theorem

Using an adaptation of Qin Jiushao’s method from the 13th century, it is possible to prove that a system of linear modular equations ai1xi + · · · + ainxn = ~bi mod ~ mi, i = 1, . . . , n has integer solutions if mi > 1 are pairwise relatively prime and in each row, at least one matrix element aij is relatively prime to mi. The Chinese remainder theorem is the special case, where A has only one...