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Miklos Schweitzer 1963_3

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September 19, 2008
superior algebrasuperior algebra unsolved

Problem Statement

Let R\equal{}R_1\oplus R_2 be the direct sum of the rings R1 R_1 and R2 R_2, and let N2 N_2 be the annihilator ideal of R2 R_2 (in R2 R_2). Prove that R1 R_1 will be an ideal in every ring R~ \widetilde{R} containing R R as an ideal if and only if the only homomorphism from R1 R_1 to N2 N_2 is the zero homomorphism. [Gy. Hajos]
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