Equational identities of the $(+,*,0,1)$ reducts of rings

Question

This is a follow up to my previous question on the equational identities of the $(+,*,0,1)$ reducts of commutative rings. In this question, I want to consider the equational identities of the $(+,*,0,1)$ reducts of rings, not necessarily commutative. I conjecture that

1. $x+0=x$
2. $x+y=y+x$
3. $(x+y)+z=x+(y+z)$
4. $x*1=x$
5. $1*x=x$
6. $(x*y)*z=x*(y*z)$
7. $x*(y+z)=(x*y)+(x*z)$
8. $(x+y)*z=(x*z)+(y*z)$
9. $x*0=0$
10. $0*x=0$

is a sufficient finite basis. Is this true?