Ring $R_{ 5 }$

$\mathbb H$: Hamilton's quaternions


Set of complex matrices $\left[\begin{smallmatrix}a&b\\-\bar b&\bar a\end{smallmatrix}\right]$, OR the real Clifford algebra for real space of signature (-,-)

Keywords matrix ring subring


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  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    cardinality $\mathfrak{c}$
    composition length left: 1right: 1
    global dimension left: 0right: 0
    Krull dimension (classical) 0
    uniform dimension left: 1right: 1
    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 $\{0\}$