Abstract structures in stochastic arithmetic

International audienceIn this work we study relevant ringoid structures in stochastic arithmetic involving multiplication. The study of such structures are needed in order to solve linear problems involving stochastic numbers in the matrix and not only in the right-hand side as it was formerly studied. This continues and extends a previous work where it has been shown that computation with generalized stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. This allowed us to solve certain practical problems with stochastic numbers and to compare algebraically obtained results with practical applications of stochastic numbers. So this theoretical works aims at extending the results obtained with the vector space structure to corresponding operations in a ring-like structure