Ring $R_{ 140 }$

Division ring with an antihomomorphism but no involution


Let $K$ and $M$ be splitting fields of $x^4+5x+5$ and $x^3-18x+18$ over $\mathbb Q$, and let $K=MF$. Then $Gal(M/F)$ is cyclic with a generator $\sigma$ with order 3. The cyclic algebra $D=(M/F,\sigma,11)$

Keywords cyclic algebra


  • P. J. Morandi, B. A. Sethuraman, and J.-P. Tignol. Division algebras with an anti-automorphism but with no involution. (2005) @ Last example before section 3.2 on p 4

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
global dimension left: 0right: 0
Krull dimension (classical) 0
weak global dimension 0
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $R$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $R$
Units $R\setminus\{0\}$
Zero divisors $\{0\}$