Ring detail


Name: $F_2[\mathcal Q_8]$

Description: Group ring of the quaternion group $\mathcal Q_8$ with the field of two elements $F_2$.

Keywords group ring

Reference(s):

  • G. Marks. Reversible and symmetric rings. (2002) @ (page needed)



Legend
  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
cardinality 256
Krull dimension (classical) 0
Name Description
Idempotents $\{0,1\}$
Jacobson radical Elements of "even weight"
Left socle $\{0, \sum_{g\in \mathcal Q_8}g\}$
Nilpotents Elements of "even weight"
Right socle $\{0, \sum_{g\in \mathcal Q_8}g\}$
Unique maximal ideal Elements of "even weight"
Units elements of "odd weight"
Zero divisors Elements of "even weight"