Examples concerning absolute flatness and amalgamation in pomonoids

Epimorphisms, dominions and amalgamation in pomonoids

“…Flatness and amalgamation properties of monoids are severely affected by the introduction of order (see [1] for details). Here we noticed that orders do not affect epimorphisms, closure properties and hence the special amalgamation of monoids.…”

“…We shall prove Claim 1 by showing that dom S (U ) = U implies dom S (U ) = U ; note that f : S −→ T is an epimorphism of pomonoids (respectively monoids) iff dom T (Im f ) = T (respectively dom T (Im f ) = T ). In what follows we shall also frequently refer to the following notions (see [1]). …”

Zigzag Theorem for Partially Ordered Monoids

“…To obtain R , define first on X S , cf. [4], a relation ZIGZAG THEOREM FOR POMONOIDS 2561 where I X denotes the identity relation on X S . Define next a relation ≤…”