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.

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