A note on subdirectly irreducible rings

Shalom Feigelstock

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let R be a commutative subdirectly irreducible ring, with minimal ideal M. It is shown that either R is a field, or M2 = 0. A construction is given which yields commutative sub-directly irreducible rings possessing nonzero-divisors, and nonzero nilpotent elements either with a unity element, or without. Such a ring without unity has been constructed by Divinsky. The same technique enables the construction of subdirectly irreducible rings with mixed additive groups.

Original languageEnglish
Pages (from-to)137-141
Number of pages5
JournalBulletin of the Australian Mathematical Society
Issue number1
StatePublished - Aug 1984


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