Nildempotency Structure of Partial One-One Contraction πΆπΌπ Transformation Semigroups
Sulaiman Awwal Akinwunmi, Morufu Mogbolagade Mogbonju, Adenike Olusola Adeniji, D.O. Oyewola, G. Yakubu, Garba Risqot Ibrahim, M. O. Fatai Β· International journal of research and scientific innovation Β· 2021
The principal objects of interest in the current research are the finite sets and the contraction ππ π§ finite transformation semigroups and the characterization of nildempotent elements in ππ π§ .Let π π§ be a finite set, say π π§ = {π¦ π , π¦ π , β¦ π¦ π§ }, where π¦ π’ is a non-negative integer then π β ππ π§ for which for all πͺ, π€ β π π§ , |ππͺ -ππ€| β€ |πͺ -π€| is a contraction mapping for all πͺ, π€ β π π , provided that any element in π(π) is not assumed to be mapped to empty as a contraction.We show that π β ππ π§ is nildempotent if there exist some minimal (nildempotent degree) π¦, π€ β ππ π§ such that π π¦ = β βΉ π π€ = π where ππ π§ = π then π π = π = π§ π = β implies π π β |π(π)| where ππππ π§ = π for each π§ β π.Then πππ π§ = π π€ π€ -π§ + π , π§, π€ β π for 1β₯ π€ β₯ π§.