Abstract
Rings in which all accessible subrings are ideals (i.e., rings in which the relation of being an ideal is transitive) are called filial. This article concerns embeddings of filial rings. We prove that every commutative reduced filial ring is an ideal in some commutative reduced filial ring with unit. This is a partial answer to the question posed by the second author on the conference Radicals of Rings and Related Topics (cf. [11], talk of K. Pryszczepko) and it is an essential generalization of Theorem 2.1 from [2].
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