A morphism of difference rings is a morphism of rings that commutes with \ sigma.
2.
The role of difference rings in difference algebra is similar to the role of commutative rings in commutative algebra and algebraic geometry.
3.
A " difference ring " is a commutative ring R together with a ring endomorphism \ sigma \ colon R \ to R.
4.
A " difference algebra " over a difference field K is a difference ring R with a K-algebra structure such that K \ to R is a morphism of difference rings, i . e . \ sigma \ colon R \ to R extends \ sigma \ colon K \ to K.
5.
A " difference algebra " over a difference field K is a difference ring R with a K-algebra structure such that K \ to R is a morphism of difference rings, i . e . \ sigma \ colon R \ to R extends \ sigma \ colon K \ to K.
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