Ring detail


Name: Right-not-left nonsingular ring

Description: Triangular ring $\begin{bmatrix}\mathbb Z&\mathbb Z/(2)\\ 0&\mathbb Z/(2)\end{bmatrix}$

Notes:

Keywords triangular ring

Reference(s):

  • (Citation needed)


  • The ring lacks the following properties:
    $\pi$-regular $I_0$ Abelian Artinian (left) Artinian (right) Baer Bezout (left) Bezout (right) Bezout domain (left) Bezout domain (right) clean cogenerator ring (left) cogenerator ring (right) commutative continuous (left) continuous (right) distributive (left) distributive (right) division ring domain dual (left) dual (right) duo (left) duo (right) exchange FI-injective (left) FI-injective (right) finite free ideal ring (left) free ideal ring (right) Frobenius fully prime fully semiprime hereditary (left) hereditary (right) Kasch (left) Kasch (right) local nonsingular (left) Ore domain (left) Ore domain (right) perfect (left) perfect (right) primary prime primitive (left) primitive (right) principal ideal domain (left) principal ideal domain (right) principal ideal ring (left) principal ideal ring (right) principally injective (left) principally injective (right) pseudo-Frobenius (left) pseudo-Frobenius (right) quasi-Frobenius reduced reversible Rickart (left) self-injective (left) self-injective (right) semi free ideal ring semicommutative (SI condition, zero-insertive) semihereditary (left) semihereditary (right) semilocal semiperfect semiprimary semiprime semiprimitive semiregular semisimple serial (left) serial (right) simple simple Artinian strongly $\pi$-regular strongly connected strongly regular symmetric top regular top simple top simple Artinian uniform (left) uniform (right) unit regular V ring (left) V ring (right) valuation ring (left) valuation ring (right) von Neumann regular Zorn