@article{Chen2024, 
author = {Hui Chen},
title = {Characterizations of normal cancellative monoids},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {302-318},
keywords = {cancellative monoids, Green's relations, normal cancellative monoids, NCM-system},
url = {https://www.sciopen.com/article/10.3934/math.2024018},
doi = {10.3934/math.2024018},
abstract = {Normal cancellative monoids were introduced to explore the general structure of cancellative monoids, which are innovative and open up new possibilities. Specifically, we pointed out that the Green's relations in a cancellative monoid    S are determined by its unitary subgroup    U to a great extent. The specific composition of egg boxes in    S, derived from the general semigroup theory, can be settled by the subgroups of    U. We call a cancellative monoid normal when these subgroups are normal and characterize it as an NCM-system. This NCM-system was created in this article and can be obtained by combining a group and a condensed cancellative monoid. Furthermore, we introduced the concept of torsion extension and proved that a special kind of normal cancellative monoids can be constructed delicately by the outer automorphism groups of given groups and some simplified cancellative monoids.}
}