Partial Order in the Normal Category Arising from Normal Bands
Advances in Mathematics: Scientific Journal, Volume 9, 2020 The notion of normal category was introduced by KSS Nambooripad in connection with the study of the structure of regular semigroups using cross connections\cite{nambooripad1994theory}. It is an abstraction of the category of principal left...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
03.05.2021
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Subjects | |
Online Access | Get full text |
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Summary: | Advances in Mathematics: Scientific Journal, Volume 9, 2020 The notion of normal category was introduced by KSS Nambooripad in connection
with the study of the structure of regular semigroups using cross
connections\cite{nambooripad1994theory}. It is an abstraction of the category
of principal left ideals of a regular semigroup. A normal band is a semigroup
$B$ satisfying $a^2=a$ and $abca=acba$ for all $a,b,c \in B$. Since the normal
bands are regular semigroups, the category $\mathcal{L}(B)$ of principal left
ideals of a normal band $B$ is a normal category. One of the special properties
of this category is that the morphism sets admit a partial order compatible
with the composition of morphisms. In this article we derive several properties
of this partial order and obtain a new characterization of this partial order. |
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DOI: | 10.48550/arxiv.2105.01135 |