Ring $R_{ 59 }$

Malcev's nonembeddable domain


The monoid ring $\Bbb Q[M]$ where $M$ is the quotient monoid $F(a,b,c,d,x,y,u,v)/С$, $F(\ldots)$ is the free monoid on those $8$ symbols and $C$ is the congruence generated by $ax = by$, $cx = dy$, $au = bv$. (See section 2 of Malcev's paper cited here.)

Notes: This is a domain that is not a subring of any division ring.

Keywords monoid ring


  • A. Malcev. On the immersion of an algebraic ring into a field. (1937) @ Section 3

  • = has the property
  • = does not have the property
  • = information not in database
Name Measure
composition length left: $\infty$right: $\infty$
Name Description
Idempotents $\{0,1\}$
Jacobson radical $\{0\}$
Left singular ideal $\{0\}$
Left socle $\{0\}$
Nilpotents $\{0\}$
Right singular ideal $\{0\}$
Right socle $\{0\}$
Zero divisors $\{0\}$