Ring detail


Name: Full linear ring of a countable dimensional right vector space

Description: Let $V$ be a countable dimensional right vector space over a division ring $D$. $R=End(V_D)$.

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

Keywords endomorphism ring ring of functions

Reference(s):

  • (Citation needed)


  • The ring lacks the following properties:
    2-primal Abelian ACC annihilator (left) ACC annihilator (right) ACC principal (left) ACC principal (right) Artinian (left) Artinian (right) Bezout domain (left) Bezout domain (right) cogenerator ring (left) cogenerator ring (right) cohopfian (left) cohopfian (right) commutative DCC annihilator (left) DCC annihilator (right) Dedekind finite distributive (left) distributive (right) division ring domain dual (left) dual (right) duo (left) duo (right) finite finite uniform dimension (left) finite uniform dimension (right) finitely cogenerated (left) finitely cogenerated (right) free ideal ring (left) free ideal ring (right) Frobenius Goldie (left) Goldie (right) hereditary (right) IBN Kasch (left) Kasch (right) local NI (nilpotents form an ideal) Noetherian (left) Noetherian (right) Ore domain (left) Ore domain (right) orthogonally finite perfect (left) perfect (right) primary principal ideal domain (left) principal ideal domain (right) principal ideal ring (left) principal ideal ring (right) pseudo-Frobenius (left) pseudo-Frobenius (right) quasi-duo (left) quasi-duo (right) quasi-Frobenius reduced reversible self-injective (left) semi free ideal ring semicommutative (SI condition, zero-insertive) semilocal semiperfect semiprimary semisimple serial (left) serial (right) simple simple Artinian simple socle (left) simple socle (right) stable range 1 stably finite strongly $\pi$-regular strongly connected strongly regular symmetric top simple Artinian uniform (left) uniform (right) unit regular V ring (left) valuation ring (left) valuation ring (right)