Assertion: abelian group's element | /r/HasProperty | necessary
Facets:
value: for some element
type: OTHER
Source sentences:
text: Next one defines an equivalence relation on M × M {\displaystyle M\times M} , such that ( m 1 , m 2 ) {\displaystyle (m_{1},m_{2})} is equivalent to ( n 1 , n 2 ) {\displaystyle (n_{1},n_{2})} if, for some element k of M, m 1 + n 2 + k = m 2 + n 1 + k (the element k is necessary because the cancellation law does not hold in all monoids).