Riesz and pre-Riesz monoids
M Zafrullah - Algebra universalis, 2022 - Springer
Call a directed partially ordered cancellative divisibility monoid M a Riesz monoid if for all x,
y_ 1, y_ 2 ≥ 0 x, y 1, y 2≥ 0 in M, x ≤ y_ 1+ y_ 2 ⇒ x= x_ 1+ x_ 2 x≤ y 1+ y 2⇒ x= x 1+ x 2 …
y_ 1, y_ 2 ≥ 0 x, y 1, y 2≥ 0 in M, x ≤ y_ 1+ y_ 2 ⇒ x= x_ 1+ x_ 2 x≤ y 1+ y 2⇒ x= x 1+ x 2 …