# Answer to Question #17651 in Abstract Algebra for Hym@n B@ss

Question #17651

Show that for any ring R, soc(R) is an ideal of R.

Expert's answer

For any minimal left ideal

*I**⊆**R*and any*r**∈**R*,*Ir*is a homomorphic image of*RI*,so*Ir*is either 0 or another minimal left ideal. Since soc(*RR*)=(sum)*I*, we see that soc(*RR*) is an ideal.Need a fast expert's response?

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