TY - JOUR

T1 - A note on subdirectly irreducible rings

AU - Feigelstock, Shalom

PY - 1984/8

Y1 - 1984/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84974098018&partnerID=8YFLogxK

U2 - 10.1017/S0004972700001799

DO - 10.1017/S0004972700001799

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AN - SCOPUS:84974098018

SN - 0004-9727

VL - 30

SP - 137

EP - 141

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 1

ER -