This paper discusses maximal and almost maximal rings in a non-commutative setting. Annihilators ideals in chain rings and their relationship to the concept of self-injectivity are investigated. In particular, a two-sided chain ring is right self-injective if and only if it is right co-Hopfian and a left maximal ring. Finally, localizations of chain rings are discussed.
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Ulrich Albrecht, Francisco Javier Santillán-Covarrubias, A note on almost maximal chain rings. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 1–11DOI 10.4171/RSMUP/52