Ring $R_{ 15 }$

Full linear ring of a countable dimensional right vector space


Let $V$ be a countable dimensional right vector space over $\mathbb Q$. $R=End(V_\mathbb Q)$, written on the left. In other words, the column-finite infinite matrices indexed by $\mathbb N$ over $\mathbb Q$.

Notes: Has exactly three ideals: the nontrivial one is the set of transformations with finite dimensional range.

Keywords endomorphism ring ring of functions


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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: $\infty$right: $\infty$
    Krull dimension (classical) 1
    weak global dimension 0
    Name Description
    Jacobson radical $\{0\}$
    Left singular ideal $\{0\}$
    Right singular ideal $\{0\}$