Unit regularity of semigroup of normal cones
Authors :
Namitha Sara Mathew 1 *, A.R. Rajan 2 and K.S. Zeenath 3
Author Address :
1 Department of Mathematics, St. Joseph’s College for Women, Alappuzha-688001, Kerala, India.
2 State Encyclopedia Institute, Government of Kerala and Department of Mathematics, University of Kerala, Thiruvananthapuram-695581, Kerala, India.
3 SDE, University of Kerala, Thiruvananthapuram-695581, Kerala, India.
*Corresponding author.
Abstract :
Let $S$ be a unit regular semigroup and $\categls$ be the normal category of principal left ideals of $S.$ Then the semigroup $T\categls$ of normal cones in $\categls$ is a unit regular semigroup. We characterize the category of principal left ideals of a unit regular semigroup as a $\ucateg$ -category. This is a normal category $\categc$ with the additional property that there is a maximum object $m$ in $v\categc$ and that every isomorphism in $\categc$ is the restriction of an isomorphism of $m.$ We prove that in this case the semigroup $T\categc$ is a unit regular semigroup.
Keywords :
Unit regular semigroup, normal category, normal cone, semigroup of normal cones.
DOI :
Article Info :
Received : September 25, 2020; Accepted : November 14, 2020.
