PARTIAL ORDER IN THE NORMAL CATEGORY ARISING FROM NORMAL BANDS
C. S. Preenu, Akhila Rajan, K. S. Zeenath · Advances in Mathematics Scientific Journal · 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 [4].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 ∈ B. Since the normal bands are regular semigroups, the category 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.