@article{Wazzan2026, 
author = {Suha Wazzan and David A. Oluyori},
title = {Flows, skew pairs and partial flows in regular semigroups},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20103-20142},
keywords = {regular semigroups, flow monoids, skew pairs of idempotents, Cauchy categories, bipartite categories, partial transformation semigroups, Rees matrix semigroups, Brandt semigroups, inverse semigroups, categorical invariants},
url = {https://www.sciopen.com/article/10.3934/math.2026817},
doi = {10.3934/math.2026817},
abstract = {This work connected flows on regular semigroups with skew pairs of idempotents via the bipartite category    β  (  S  ), where arrows    e      →          s        f exist if and only if some inverse        s    ′   satisfies    e  =  s      s    ′   and    f  =      s    ′    s. Partial flows satisfying    a  b  a  =  a and    b  a  b  =  b were introduced. Using Luangchaisam and Changphas' theorem, explicit partial flows were constructed for strong, left regular, and right regular skew pairs, with domain sizes    1,    2 and    2, respectively. Flow monoids were classified for groups (   Φ  (  G  )  ≅  G), rectangular bands, Brandt semigroups (   Φ  (      B    n    )  ≅      T    n  ), inverse semigroups, and completely simple semigroups, where the sandwich matrix twists composition. The discrete skew pair case remains open.}
}