Ring detail


Name: $k[[x]]$

Description: Ring of formal power series over a field $k$

Notes:

Keywords power series ring

Reference(s):

  • (Citation needed)


  • This ring has the following properties:
    $I_0$ 2-primal Abelian ACC annihilator (left) ACC annihilator (right) ACC principal (left) ACC principal (right) Baer Bezout (left) Bezout (right) Bezout domain (left) Bezout domain (right) clean coherent (left) coherent (right) commutative connected CS (left) CS (right) DCC annihilator (left) DCC annihilator (right) Dedekind finite distributive (left) distributive (right) domain duo (left) duo (right) exchange finite uniform dimension (left) finite uniform dimension (right) finitely generated socle (left) finitely generated socle (right) free ideal ring (left) free ideal ring (right) Goldie (left) Goldie (right) hereditary (left) hereditary (right) IBN Ikeda-Nakayama (left) Ikeda-Nakayama (right) lift/rad local NI (nilpotents form an ideal) Noetherian (left) Noetherian (right) nonsingular (left) nonsingular (right) Ore domain (left) Ore domain (right) Ore ring (left) Ore ring (right) orthogonally finite polynomial identity prime principal ideal domain (left) principal ideal domain (right) principal ideal ring (left) principal ideal ring (right) quasi-continuous (left) quasi-continuous (right) quasi-duo (left) quasi-duo (right) reduced reversible Rickart (left) Rickart (right) semi free ideal ring semicommutative (SI condition, zero-insertive) semihereditary (left) semihereditary (right) semilocal semiperfect semiprime semiregular serial (left) serial (right) stable range 1 stably finite strongly connected symmetric top regular top simple top simple Artinian uniform (left) uniform (right) valuation ring (left) valuation ring (right) weakly clean