Abstract.
A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We prove that every ring which is a left essential extension of a reduced ring is a subdirect sum of rings which are essential extensions of domains, but the converse implication does not hold. We give some applications of this result and discuss several related questions.
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Received: 6 January 2003
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Beidar, K.I., Fong, Y. & Puczyłowski, E.R. On essential extensions of reduced rings and domains. Arch. Math. 83, 344–352 (2004). https://doi.org/10.1007/s00013-003-4786-x
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DOI: https://doi.org/10.1007/s00013-003-4786-x