# Ring detail

## Name: Left-not-right valuation domain

Description: Let $k$ be a field, and $F$ be the field of rational functions for $k(t_0, t_1,\ldots)$ in countably many variables. $\alpha$ is the injective homomorphism such that $\alpha(t_i)=t_{i+1}$, and $t_0$ is transcendental over $\alpha(F)$. Let $A$ be the ring generated by $\frac{f}{1+gy}$ where $f,g\in A[y]$. We can extend $\alpha$ to $\phi:A\to A$ by the rule $\phi(y)=t$. The ring is $R=A[[x;\phi]]$, the skew-powerseries ring using $xa=\phi(a)x$.

Keywords subring twisted (skew) ring

Reference(s):

• A. A. Tuganbaev. Semidistributive modules and rings. (2012) @ Example 9.10 p 213

Legend
• = has the property
• = does not have the property
• = information not in database

(Nothing was retrieved.)

(Nothing was retrieved.)