A right ideal I of a ring R is said to be a comparizer right ideal of R if for any right ideals A, B of R, either A subset of B or BI subset of A. A ring R (with 1) is called a right pseudo-chain ring if for any nonunit a is an element of R, aR is a comparizer right ideal of R. These rings are generalizations of right chain rings and commutative pseudo-valuation rings. In this paper we study the structure of right pseudo-chain rings. We prove that a ring R containing a non-zero-divisor in the Jacobson radical J(R) is a pseudo-chain ring if and only if R is a local subring of a (unique up to isomorphism) chain ring T with J(T) = J(R). We also introduce the concept of a pseudo-uniserial module.
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