(eng): There are proven generalizations of the Hölder’s and Minkowski’s inequalities for the pseudo-integral. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g, the second semiring ([a, b], sup, circled dot operator), where circled dot operator is generated and the third semiring where both pseudo-operations are idempotent, i.e., circled plus = sup and circled dot operator = inf.