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Regularity of semilattice sums of rings

1973
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Proceedings of the American Mathematical Society
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If R is a supplementary semilattice sum of subrings Ra, a e Cl, then R is regular if and only if each Rat is regular. A ring is said to be regular, in the sense of von Neumann [6], if for each a e R there exists x e R such that axa=a. The concept of (supplementary) semilattice sum is defined in the previous article [8]. In this article, we prove that if R is a supplementary semilattice sum of subrings Rx, a e £2, then R is regular if and only if Rx is regular for every a e £2. We state, without

doi:10.1090/s0002-9939-1973-0316495-1
fatcat:lv6f2h2kzzcp7kcjhd27qo5htm