1988 Penny possible error?

Can anyone tell me what the ring is that goes around this penny on the front and back?

 

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That is from die deterioration, the dies used to strike the coin were nearing the end of their lives.

 

I agree.. The periphery of your 1988 cent shows development of a “ridge ring”, a form of die wear common in zinc cents. On your Cent the field portion of the die has retreated, and this has resulted in thinning of the motto IN GOD WE TRUST.