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A note on almost maximal chain rings. (English) Zbl 1479.16016

Summary: 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.

MSC:

16L30 Noncommutative local and semilocal rings, perfect rings
16D50 Injective modules, self-injective associative rings
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)
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