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A condition for a semiprime ring to be Artinian. (Chinese) Zbl 0995.16502
Summary: We prove the following theorem. Let Ω be a semiprime ring, A an ideal of Ω with identity element. If the principal left ideals of Ω contained in A almost satisfy the descending chain condition, then A is a Jacobson semisimple Artinian ring.
MSC:
16N60Prime and semiprime associative rings
16P20Associative Artinian rings and modules
16D252-sided ideals (associative rings and algebras)
16P70Chain conditions on other classes of submodules, etc.