Let 𝑅 be a ring such that 𝑅𝑅 = 𝑒1𝑅 ⊕ · · · ⊕ 𝑒𝑛𝑅, where each 𝑒𝑖𝑅 is a uniform right ideal and {𝑒𝑖 | 1 ≤ 𝑖 ≤ 𝑛} is a set of idempotents. We consider the following condition on 𝑅𝑅: for all 𝑖, 𝑗 ∈ {1, . . . , 𝑛}, the module 𝑒𝑖𝑅 does not embed in any proper submodule of 𝑒 𝑗 𝑅. A ring satisfying this condition is called a right (𝑃)-ring. In this paper, we prove that the following conditions are equivalent for a ring 𝑅: (i) 𝑅 is a quasi-Frobenius (QF) ring; (ii) 𝑅 is right Noetherian, right countably Σ-CS, and a right (𝑃)-ring.