Ring $R_{ 118 }$

Cozzens simple, left principal, right non-Noetherian domain


The construction is a skew polynomial ring $E[t, \rho,\delta]$ where $E$ is a field of characteristic $0$, $\rho$ is a monomorphism $E\to E$, and $\delta$ is a $\rho$-derivation of $E$, that is, an additive map that also satisfies $\delta(ab)=\rho(a)\delta(b)+\delta(a)b$. The set of polynomials $E[t]$ is given a new multiplication that satisfies $ta=\rho(a)t+\delta(a)$. (Specifics about $E$, $\rho$ and $\delta$ to follow.)

Keywords twisted (skew) polynomial ring


  • J. H. Cozzens. Simple principal left ideal domains. (1972) @ (entire paper)

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Name Measure
global dimension left: 1right:
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$