Composition rings from formal power series rings

ABSTRACT

We study the ideals in some Dickson nearrings of polynomials and formal power series. For some of their related quotients, we introduce variants and generalizations, and construct composition rings also.

KEYWORDS:

• Composition ring
• coupling map
• Dickson nearring
• formal power series

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16Y30

Notes

¹For us, ℕ₀ is the set of natural numbers including 0.

²We observe that, because of the hypothesis for which T is an automorphism (and A is a skew-field) we have $D_n=X^n\cdot B=X^n\circ B=B\circ X^n=B\cdot X^n$.

³As usual, $\overline{G}$ denotes the natural extension of G to R[[X]].

⁴We always understand the function ρ to fulfill the property that ρ(0) = 0.

⁵Obviously, condition (5) implies condition (4)